Special Right Triangles Geometry 7 3 Special Right
- Slides: 46
Special Right Triangles Geometry 7 -3
Special Right Triangles 45 – 45 - 90 Geometry 7 -3 a
Review
Areas
• Area of a Triangle The area of a triangle is given by the formula A = ½ B x H, where A is the area, B is the length of the base, and H is the height of the triangle Area
• The Pythagorean theorem In a right triangle, the sum of the squares of the legs of the triangle equals the square of the hypotenuse of the triangle B c a C Theorem b A
• Converse of the Pythagorean theorem If the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle. B c a C Theorem b A
Converse of Pythagorean
New Material
• Copy the following chart into your notes Investigation
• Find the length of the hypotenuse of each isosceles right triangle. Simplify each square root. • Record the answers in your chart Investigation
• Finish the chart for each of the listed leg lengths Investigation
• 45° – 90° Triangle In a 45° – 90° triangle the hypotenuse is the square root of two times as long as each leg Theorem
Question When the problem says this, How do we reduce the square root of two? Answer We don’t, unless it is in the denominator.
• Know the basic triangle • Set known information equal to the corresponding part of the basic triangle • Solve for the other sides
Example
Practice
Example
Practice
Practice
Practice
Practice
Practice
Special Right Triangles 30 – 60 - 90 Geometry 7 -3 b
Draw This in your notes A large equilateral triangle Special Triangle Investigation
Divide the triangle in half You now have a 30° – 60° – 90° triangle Special Triangle Investigation
Label the triangle. Special Triangle Investigation
Is AC = BC? Why? Yes, Definition of isosceles triangle, or equilateral Special Triangle Investigation
Are the two separate triangles congruent? Why? Yes, ASA Special Triangle Investigation
Is AD = BD? Why? Yes, CPCTC Special Triangle Investigation
So, AC = AB, and AD = DB; What is the relationship between AC and AD? AC = 2 x AD Special Triangle Investigation
So AC = 2 AD Using the Pythagorean theorem, what is the length of CD, in terms of AD? Special Triangle Investigation
• 30° – 60° – 90° Triangle In a 30° – 60° – 90° triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is the square root of three times as long as the shorter leg Theorem
• Know the basic triangles • Set known information equal to the corresponding part of the basic triangle • Solve for the other sides Solving Strategy
• Know the basic triangles • Set known information equal to the corresponding part of the basic triangle • Solve for the other sides
Example
Example
Practice
Practice
Practice
Practice
Practice
Practice
Practice
Practice
• Pages 369 – 372 • 2 – 8 even, 12 – 28 even, 34 – 38 even, 47, 48 Homework
- Solving special right triangles
- Special right triangles activity
- 8-3 special right triangles answer key
- Right product right place right time right price
- Family time
- Special right triangles in real life
- Special right triangles video
- 5-8 applying special right triangles
- Special right triangles simplest radical form
- Parts of a triangle
- 5-8 practice b applying special right triangles
- Six trigonometric ratios
- Trig special right triangles
- Special triangles 45 45 90
- Unit 3 lesson 2 special right triangles
- 8-4 special right triangles
- 5-8 applying special right triangles
- 8-3 lesson quiz geometry
- Applying special right triangles
- A2+b2=c2
- Lesson 7-3 triangles
- 7-3 practice special right triangles
- 45-45-90 triangle notes
- 5-8 applying special right triangles
- Simplest radical form of 45
- Applying special right triangles
- 7-3 practice special right triangles answers
- Special right triangles investigation
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- This molecule is
- Pf3 number of vsepr electron groups
- Electron domain geometry vs molecular geometry
- Geometry 3-5 parallel lines and triangles
- Geometry unit 5 homework 1 triangle midsegments
- Geometry classifying triangles
- Sss~ (or sas~)
- Parallel lines and triangles 3-5
- Isosceles triangle algebra
- Special segments in triangles
- Special lines in triangles
- Benchmark angle measurements
- Special lines in triangles
- Ratios of special triangles calculator
- Special segments in triangles
- Special triangle
- How to label hyp opp adj
- Real world examples of complementary angles