Percentage Percentage Percentage Find each amount a 12
![Percentage Percentage](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-1.jpg)
![Percentage Percentage](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-2.jpg)
![Percentage Find each amount. a) 12% of 40 c) 5% of 320 m e) Percentage Find each amount. a) 12% of 40 c) 5% of 320 m e)](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-3.jpg)
![Percentage Find each percent. a) 40 out of 200 b) 75 g out of Percentage Find each percent. a) 40 out of 200 b) 75 g out of](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-4.jpg)
![Word Problem 1. Fred earned $325 last year working at the Pizza Boat. He Word Problem 1. Fred earned $325 last year working at the Pizza Boat. He](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-5.jpg)
![DISCOUNT AND SALES TAX DISCOUNT AND SALES TAX](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-6.jpg)
![](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-7.jpg)
![Outline: • Ratios! What is a Ratio? How to Use Ratios? How to Simplify? Outline: • Ratios! What is a Ratio? How to Use Ratios? How to Simplify?](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-8.jpg)
![Ratios and Proportions Ratios and Proportions](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-9.jpg)
![Outline: • Ratios! What is a Ratio? How to Use Ratios? How to Simplify? Outline: • Ratios! What is a Ratio? How to Use Ratios? How to Simplify?](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-10.jpg)
![What is a Ratio? • A ratio is a comparison of two numbers. • What is a Ratio? • A ratio is a comparison of two numbers. •](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-11.jpg)
![How to Use Ratios? • The ratio of boys and girls in the class How to Use Ratios? • The ratio of boys and girls in the class](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-12.jpg)
![How to simplify ratios? • The ratios we saw on last slide were all How to simplify ratios? • The ratios we saw on last slide were all](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-13.jpg)
![How to simplify ratios? • Now I tell you I have 12 cats and How to simplify ratios? • Now I tell you I have 12 cats and](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-14.jpg)
![How to simplify ratios? A person’s arm is 80 cm, he is 2 m How to simplify ratios? A person’s arm is 80 cm, he is 2 m](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-15.jpg)
![How to simplify ratios? • Let’s try m now! Once we have the same How to simplify ratios? • Let’s try m now! Once we have the same](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-16.jpg)
![How to simplify ratios? • If the numerator and denominator do not have the How to simplify ratios? • If the numerator and denominator do not have the](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-17.jpg)
![More examples… = = = More examples… = = =](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-18.jpg)
![Now, on to proportions! What is a proportion? A proportion is an equation that Now, on to proportions! What is a proportion? A proportion is an equation that](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-19.jpg)
![Properties of a proportion? Cross Product Property 2 x 6=12 3 x 4 = Properties of a proportion? Cross Product Property 2 x 6=12 3 x 4 =](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-20.jpg)
![Properties of a proportion? • Cross Product Property ad = bc means extremes Properties of a proportion? • Cross Product Property ad = bc means extremes](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-21.jpg)
![Properties of a proportion? Let’s make sense of the Cross Product Property… For any Properties of a proportion? Let’s make sense of the Cross Product Property… For any](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-22.jpg)
![Properties of a proportion? • Reciprocal Property If Then Can you see it? If Properties of a proportion? • Reciprocal Property If Then Can you see it? If](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-23.jpg)
![How about an example? Solve for x: 7(6) = 2 x 42 = 2 How about an example? Solve for x: 7(6) = 2 x 42 = 2](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-24.jpg)
![How about another example? Solve for x: 7 x = 2(12) Cross Product Property How about another example? Solve for x: 7 x = 2(12) Cross Product Property](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-25.jpg)
![Can you solve this one? Solve for x: 7 x = (x-1)3 Cross Product Can you solve this one? Solve for x: 7 x = (x-1)3 Cross Product](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-26.jpg)
![Now you know enough about properties, let’s solve the Mysterious problems! If your car Now you know enough about properties, let’s solve the Mysterious problems! If your car](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-27.jpg)
![5 miles to home 5 miles to school So you use up 1/3 gallon 5 miles to home 5 miles to school So you use up 1/3 gallon](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-28.jpg)
![So you use up 5/3 gallons a week (which is about 1. 67 gallons). So you use up 5/3 gallons a week (which is about 1. 67 gallons).](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-29.jpg)
![So what do you think? 5 miles 10 miles You pay about 6 bucks So what do you think? 5 miles 10 miles You pay about 6 bucks](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-30.jpg)
![Geometric Relationships Geometric Relationships](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-31.jpg)
![Classify Polygons Polygon – is a closed figure formed by three or more line Classify Polygons Polygon – is a closed figure formed by three or more line](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-32.jpg)
![Regular quadrilateral Regular quadrilateral](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-33.jpg)
![Regular and Irregular quadrilateral Regular and Irregular quadrilateral](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-34.jpg)
![Angle Properties • When two lines intersect , the opposites angles are equal Angle Properties • When two lines intersect , the opposites angles are equal](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-35.jpg)
![• The sum of the interior angles of a triangle is 180 degree. • The sum of the interior angles of a triangle is 180 degree.](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-36.jpg)
![What is x? What is x?](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-37.jpg)
![Alternate angles are equal Alternate angles are equal](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-38.jpg)
![Corresponding angles are equal Corresponding angles are equal](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-39.jpg)
![Co-interior angles have a sum of 180 degree Co-interior angles have a sum of 180 degree](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-40.jpg)
![Angle Relationships in Triangles • Vertex – point where two or more sides meet Angle Relationships in Triangles • Vertex – point where two or more sides meet](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-41.jpg)
![• Interior angle – angle formed on the inside of a polygon by • Interior angle – angle formed on the inside of a polygon by](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-42.jpg)
![Find the measure of the exterior angles of ABC Find the measure of the exterior angles of ABC](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-43.jpg)
![Find a, b, and c. Find a, b, and c.](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-44.jpg)
![Exterior Angles of a triangle • The sum of the exterior angles of a Exterior Angles of a triangle • The sum of the exterior angles of a](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-45.jpg)
![Angle Relationship is Quadrilaterals • Sum of interior angles of a quadrilateral is 360 Angle Relationship is Quadrilaterals • Sum of interior angles of a quadrilateral is 360](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-46.jpg)
![Angle Relationship of Quadrilateral • Sum or the exterior angles of a quadrilateral Angle Relationship of Quadrilateral • Sum or the exterior angles of a quadrilateral](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-47.jpg)
![Angle Relationships in Parallelograms • Adjacent – adjoining or next to • Supplementary – Angle Relationships in Parallelograms • Adjacent – adjoining or next to • Supplementary –](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-48.jpg)
![Angle Relationships in Polygons • Convex polygon – a polygon with no part of Angle Relationships in Polygons • Convex polygon – a polygon with no part of](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-49.jpg)
![Polygons • • • Pentagon – a polygon with five sides Hexagon – a Polygons • • • Pentagon – a polygon with five sides Hexagon – a](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-50.jpg)
![Polygons Polygons](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-51.jpg)
![REMEMBER REMEMBER](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-52.jpg)
![Midpoints and Medians in Triangles • Midpoint – the point that divides a line Midpoints and Medians in Triangles • Midpoint – the point that divides a line](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-53.jpg)
- Slides: 53
![Percentage Percentage](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-1.jpg)
Percentage
![Percentage Percentage](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-2.jpg)
Percentage
![Percentage Find each amount a 12 of 40 c 5 of 320 m e Percentage Find each amount. a) 12% of 40 c) 5% of 320 m e)](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-3.jpg)
Percentage Find each amount. a) 12% of 40 c) 5% of 320 m e) 4. 5% of 20 kg g) 90% of 45 g b) 18% of $36. 00 d) 21. 5% of 2500 f) 7. 5% of 360˚ h) 36% of $5. 50
![Percentage Find each percent a 40 out of 200 b 75 g out of Percentage Find each percent. a) 40 out of 200 b) 75 g out of](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-4.jpg)
Percentage Find each percent. a) 40 out of 200 b) 75 g out of 225 g c) 64 out of 16 d) 32 out of 180 e) 21 out of 100 f) 12 out of 8
![Word Problem 1 Fred earned 325 last year working at the Pizza Boat He Word Problem 1. Fred earned $325 last year working at the Pizza Boat. He](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-5.jpg)
Word Problem 1. Fred earned $325 last year working at the Pizza Boat. He spent $165. What percent of his money did he spend? 2. There are 1970 students in the school, 550 of which are grade 9 students. What percent of students are in grade 9. What percent of students are NOT in grade 9.
![DISCOUNT AND SALES TAX DISCOUNT AND SALES TAX](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-6.jpg)
DISCOUNT AND SALES TAX
![](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-7.jpg)
![Outline Ratios What is a Ratio How to Use Ratios How to Simplify Outline: • Ratios! What is a Ratio? How to Use Ratios? How to Simplify?](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-8.jpg)
Outline: • Ratios! What is a Ratio? How to Use Ratios? How to Simplify? Proportions! What is a proportion? Properties of proportions? How to use proportions? • Mysterious Problems…
![Ratios and Proportions Ratios and Proportions](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-9.jpg)
Ratios and Proportions
![Outline Ratios What is a Ratio How to Use Ratios How to Simplify Outline: • Ratios! What is a Ratio? How to Use Ratios? How to Simplify?](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-10.jpg)
Outline: • Ratios! What is a Ratio? How to Use Ratios? How to Simplify? Proportions! What is a proportion? Properties of proportions? How to use proportions? • Mysterious Problems…
![What is a Ratio A ratio is a comparison of two numbers What is a Ratio? • A ratio is a comparison of two numbers. •](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-11.jpg)
What is a Ratio? • A ratio is a comparison of two numbers. • Ratios can be written in three different ways: a to b a: b Because a ratio is a fraction, b can not be zero Ratios are expressed in simplest form
![How to Use Ratios The ratio of boys and girls in the class How to Use Ratios? • The ratio of boys and girls in the class](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-12.jpg)
How to Use Ratios? • The ratio of boys and girls in the class is 12 to 11. This means, for every 12 boys you can find 11 girls to match. How could manybe dogs cats do • There justand 12 boys, 11 I have? We don’t know, all we girls. knowcould is if they’d fight, • There be 24 start boys, a 22 girls. eachcould dog has to fight 2 cats. • There be 120 boys, 110 4 cm girls…a huge class 1 cm • The ratio of length and width of this rectangle is 4 to 1. What is the ratio if the rectangle is 8 cm long and 2 cm wide? Still 4 to 1, because for every 4 cm, you can find 1 cm to match . • The ratio of cats and dogs at my home is 2 to 1
![How to simplify ratios The ratios we saw on last slide were all How to simplify ratios? • The ratios we saw on last slide were all](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-13.jpg)
How to simplify ratios? • The ratios we saw on last slide were all simplified. How was it done? Ratios can be expressed The ratio of boys and girls in the class is The ratio of the rectangle is in fraction form… This allows us to do math on them. The ratio of cats and dogs in my house is
![How to simplify ratios Now I tell you I have 12 cats and How to simplify ratios? • Now I tell you I have 12 cats and](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-14.jpg)
How to simplify ratios? • Now I tell you I have 12 cats and 6 dogs. Can you simplify the ratio of cats and dogs to 2 to 1? = = Divide both numerator and denominator by their Greatest Common Factor 6.
![How to simplify ratios A persons arm is 80 cm he is 2 m How to simplify ratios? A person’s arm is 80 cm, he is 2 m](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-15.jpg)
How to simplify ratios? A person’s arm is 80 cm, he is 2 m tall. Find the ratio of the length of his arm to his total height To compare them, we need to convert both numbers into the same unit …either cm or m. • Let’s try cm first! Once we have the same units, we can simplify them.
![How to simplify ratios Lets try m now Once we have the same How to simplify ratios? • Let’s try m now! Once we have the same](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-16.jpg)
How to simplify ratios? • Let’s try m now! Once we have the same units, they simplify to 1. To make both numbers integers, we multiplied both numerator and denominator by 10
![How to simplify ratios If the numerator and denominator do not have the How to simplify ratios? • If the numerator and denominator do not have the](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-17.jpg)
How to simplify ratios? • If the numerator and denominator do not have the same units it may be easier to convert to the smaller unit so we don’t have to work with decimals… 3 cm/12 m = 3 cm/1200 cm = 1/400 2 kg/15 g = 2000 g/15 g = 400/3 5 ft/70 in = (5*12)in / 70 in = 60 in/70 in = 6/7 2 g/8 g = 1/4 Of course, if they are already in the same units, we don’t have to worry about converting. Good deal
![More examples More examples… = = =](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-18.jpg)
More examples… = = =
![Now on to proportions What is a proportion A proportion is an equation that Now, on to proportions! What is a proportion? A proportion is an equation that](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-19.jpg)
Now, on to proportions! What is a proportion? A proportion is an equation that equates two ratios The ratio of dogs and cats was 3/2 The ratio of dogs and cats now is 6/4=3/2 So we have a proportion :
![Properties of a proportion Cross Product Property 2 x 612 3 x 4 Properties of a proportion? Cross Product Property 2 x 6=12 3 x 4 =](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-20.jpg)
Properties of a proportion? Cross Product Property 2 x 6=12 3 x 4 = 2 x 6
![Properties of a proportion Cross Product Property ad bc means extremes Properties of a proportion? • Cross Product Property ad = bc means extremes](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-21.jpg)
Properties of a proportion? • Cross Product Property ad = bc means extremes
![Properties of a proportion Lets make sense of the Cross Product Property For any Properties of a proportion? Let’s make sense of the Cross Product Property… For any](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-22.jpg)
Properties of a proportion? Let’s make sense of the Cross Product Property… For any numbers a, b, c, d:
![Properties of a proportion Reciprocal Property If Then Can you see it If Properties of a proportion? • Reciprocal Property If Then Can you see it? If](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-23.jpg)
Properties of a proportion? • Reciprocal Property If Then Can you see it? If yes, can you think of why it works?
![How about an example Solve for x 76 2 x 42 2 How about an example? Solve for x: 7(6) = 2 x 42 = 2](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-24.jpg)
How about an example? Solve for x: 7(6) = 2 x 42 = 2 x 21 = x Cross Product Property
![How about another example Solve for x 7 x 212 Cross Product Property How about another example? Solve for x: 7 x = 2(12) Cross Product Property](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-25.jpg)
How about another example? Solve for x: 7 x = 2(12) Cross Product Property 7 x = 24 x= Can you solve it using Reciprocal Property? If yes, would it be easier?
![Can you solve this one Solve for x 7 x x13 Cross Product Can you solve this one? Solve for x: 7 x = (x-1)3 Cross Product](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-26.jpg)
Can you solve this one? Solve for x: 7 x = (x-1)3 Cross Product Property 7 x = 3 x – 3 4 x = -3 x= Again, Reciprocal Property?
![Now you know enough about properties lets solve the Mysterious problems If your car Now you know enough about properties, let’s solve the Mysterious problems! If your car](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-27.jpg)
Now you know enough about properties, let’s solve the Mysterious problems! If your car gets 30 miles/gallon, how many gallons of gas do you need to commute to school everyday? 5 miles to home 5 miles to school Let x be the number gallons we need for a day: x= Gal Can you solve it from here?
![5 miles to home 5 miles to school So you use up 13 gallon 5 miles to home 5 miles to school So you use up 1/3 gallon](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-28.jpg)
5 miles to home 5 miles to school So you use up 1/3 gallon a day. How many gallons would you use for a week? Let t be the number of gallons we need for a week: What property is this? Gal
![So you use up 53 gallons a week which is about 1 67 gallons So you use up 5/3 gallons a week (which is about 1. 67 gallons).](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-29.jpg)
So you use up 5/3 gallons a week (which is about 1. 67 gallons). Consider if the price of gas is 3. 69 dollars/gal, how much would it cost for a week? Let s be the sum of cost for a week: 3. 69(1. 67) = 1 s s = 6. 16 dollars 5 miles to home 5 miles to school
![So what do you think 5 miles 10 miles You pay about 6 bucks So what do you think? 5 miles 10 miles You pay about 6 bucks](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-30.jpg)
So what do you think? 5 miles 10 miles You pay about 6 bucks a week just to get to school! What about weekends? If you travel twice as much on weekends, say drive 10 miles to the Mall and 10 miles back, how many gallons do you need now? How much would it cost totally? How much would it cost for a month? Think proportionally!. . . It’s all about proportions!
![Geometric Relationships Geometric Relationships](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-31.jpg)
Geometric Relationships
![Classify Polygons Polygon is a closed figure formed by three or more line Classify Polygons Polygon – is a closed figure formed by three or more line](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-32.jpg)
Classify Polygons Polygon – is a closed figure formed by three or more line segments Regular polygon – has all sides equal and all angles equal Regular quadrilateral is a square. An irregular quadrilateral may be a rectangle, a rhombus, a parallelogram, or a trapezoid.
![Regular quadrilateral Regular quadrilateral](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-33.jpg)
Regular quadrilateral
![Regular and Irregular quadrilateral Regular and Irregular quadrilateral](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-34.jpg)
Regular and Irregular quadrilateral
![Angle Properties When two lines intersect the opposites angles are equal Angle Properties • When two lines intersect , the opposites angles are equal](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-35.jpg)
Angle Properties • When two lines intersect , the opposites angles are equal
![The sum of the interior angles of a triangle is 180 degree • The sum of the interior angles of a triangle is 180 degree.](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-36.jpg)
• The sum of the interior angles of a triangle is 180 degree.
![What is x What is x?](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-37.jpg)
What is x?
![Alternate angles are equal Alternate angles are equal](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-38.jpg)
Alternate angles are equal
![Corresponding angles are equal Corresponding angles are equal](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-39.jpg)
Corresponding angles are equal
![Cointerior angles have a sum of 180 degree Co-interior angles have a sum of 180 degree](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-40.jpg)
Co-interior angles have a sum of 180 degree
![Angle Relationships in Triangles Vertex point where two or more sides meet Angle Relationships in Triangles • Vertex – point where two or more sides meet](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-41.jpg)
Angle Relationships in Triangles • Vertex – point where two or more sides meet
![Interior angle angle formed on the inside of a polygon by • Interior angle – angle formed on the inside of a polygon by](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-42.jpg)
• Interior angle – angle formed on the inside of a polygon by two sides meeting at a vertex • Exterior angle – angle formed on the outside of a geometric shape by extending one of the sides past a vertex
![Find the measure of the exterior angles of ABC Find the measure of the exterior angles of ABC](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-43.jpg)
Find the measure of the exterior angles of ABC
![Find a b and c Find a, b, and c.](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-44.jpg)
Find a, b, and c.
![Exterior Angles of a triangle The sum of the exterior angles of a Exterior Angles of a triangle • The sum of the exterior angles of a](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-45.jpg)
Exterior Angles of a triangle • The sum of the exterior angles of a triangle is 360 degree.
![Angle Relationship is Quadrilaterals Sum of interior angles of a quadrilateral is 360 Angle Relationship is Quadrilaterals • Sum of interior angles of a quadrilateral is 360](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-46.jpg)
Angle Relationship is Quadrilaterals • Sum of interior angles of a quadrilateral is 360 degree
![Angle Relationship of Quadrilateral Sum or the exterior angles of a quadrilateral Angle Relationship of Quadrilateral • Sum or the exterior angles of a quadrilateral](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-47.jpg)
Angle Relationship of Quadrilateral • Sum or the exterior angles of a quadrilateral
![Angle Relationships in Parallelograms Adjacent adjoining or next to Supplementary Angle Relationships in Parallelograms • Adjacent – adjoining or next to • Supplementary –](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-48.jpg)
Angle Relationships in Parallelograms • Adjacent – adjoining or next to • Supplementary – adding to 180 degree • Transversal – line intersecting two or more lines
![Angle Relationships in Polygons Convex polygon a polygon with no part of Angle Relationships in Polygons • Convex polygon – a polygon with no part of](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-49.jpg)
Angle Relationships in Polygons • Convex polygon – a polygon with no part of any line segment joining two points on the polygon outside the polygon • Concave polygon – a polygon with parts of some line segments joining two points on the polygon outside the polygon
![Polygons Pentagon a polygon with five sides Hexagon a Polygons • • • Pentagon – a polygon with five sides Hexagon – a](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-50.jpg)
Polygons • • • Pentagon – a polygon with five sides Hexagon – a polygon with six sides Heptagon – a polygon with seven sides Octagon – a polygon with eight sides Regular polygon – a polygon with all sides equal and all interior angles equal SUM OF INTERIOR ANGLES = 180(n-2)
![Polygons Polygons](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-51.jpg)
Polygons
![REMEMBER REMEMBER](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-52.jpg)
REMEMBER
![Midpoints and Medians in Triangles Midpoint the point that divides a line Midpoints and Medians in Triangles • Midpoint – the point that divides a line](https://slidetodoc.com/presentation_image/e566cddd488562b32c610418d82b0e08/image-53.jpg)
Midpoints and Medians in Triangles • Midpoint – the point that divides a line segment into two equal segments
How to read centavos
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