QUADRILATERALS OBJECTIVES DEFINE AND CLASSIFY QUADRILATERALS ALONG WITH
![QUADRILATERALS OBJECTIVES: DEFINE AND CLASSIFY QUADRILATERALS ALONG WITH THEIR RELATED PARTS (PARALLELOGRAM, RHOMBUS, RECTANGLE, QUADRILATERALS OBJECTIVES: DEFINE AND CLASSIFY QUADRILATERALS ALONG WITH THEIR RELATED PARTS (PARALLELOGRAM, RHOMBUS, RECTANGLE,](https://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-1.jpg)
QUADRILATERALS OBJECTIVES: DEFINE AND CLASSIFY QUADRILATERALS ALONG WITH THEIR RELATED PARTS (PARALLELOGRAM, RHOMBUS, RECTANGLE, SQUARE, TRAPEZOID, KITE) Homework: Read pg. 64 -65 pg. 66 # 7 -10, 13(!)
![OBJECTIVES To identify any quadrilateral, by name, as specifically as you can, based on OBJECTIVES To identify any quadrilateral, by name, as specifically as you can, based on](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-2.jpg)
OBJECTIVES To identify any quadrilateral, by name, as specifically as you can, based on its characteristics
![QUADRILATERAL a quadrilateral is a polygon with 4 sides. QUADRILATERAL a quadrilateral is a polygon with 4 sides.](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-3.jpg)
QUADRILATERAL a quadrilateral is a polygon with 4 sides.
![SPECIFIC QUADRILATERALS There are several specific types of quadrilaterals. They are classified based on SPECIFIC QUADRILATERALS There are several specific types of quadrilaterals. They are classified based on](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-4.jpg)
SPECIFIC QUADRILATERALS There are several specific types of quadrilaterals. They are classified based on their sides or angles.
![](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-5.jpg)
![A quadrilateral simply has 4 sides – no other special requirements. A quadrilateral simply has 4 sides – no other special requirements.](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-6.jpg)
A quadrilateral simply has 4 sides – no other special requirements.
![EXAMPLES OF QUADRILATERALS EXAMPLES OF QUADRILATERALS](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-7.jpg)
EXAMPLES OF QUADRILATERALS
![A parallelogram has two pairs of parallel sides. A parallelogram has two pairs of parallel sides.](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-8.jpg)
A parallelogram has two pairs of parallel sides.
![PARALLELOGRAM Two pairs of parallel sides opposite sides are actually congruent. PARALLELOGRAM Two pairs of parallel sides opposite sides are actually congruent.](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-9.jpg)
PARALLELOGRAM Two pairs of parallel sides opposite sides are actually congruent.
![A rhombus is a parallelogram that has four congruent sides. A rhombus is a parallelogram that has four congruent sides.](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-10.jpg)
A rhombus is a parallelogram that has four congruent sides.
![RHOMBUS Still has two pairs of parallel sides; with opposite sides congruent. 4 in. RHOMBUS Still has two pairs of parallel sides; with opposite sides congruent. 4 in.](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-11.jpg)
RHOMBUS Still has two pairs of parallel sides; with opposite sides congruent. 4 in.
![A rectangle has four right angles. A rectangle has four right angles.](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-12.jpg)
A rectangle has four right angles.
![RECTANGLE Still has two pairs of parallel sides; with opposite sides congruent. Has four RECTANGLE Still has two pairs of parallel sides; with opposite sides congruent. Has four](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-13.jpg)
RECTANGLE Still has two pairs of parallel sides; with opposite sides congruent. Has four right angles
![A square is a specific case of both a rhombus AND a rectangle, having A square is a specific case of both a rhombus AND a rectangle, having](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-14.jpg)
A square is a specific case of both a rhombus AND a rectangle, having four right angles and 4 congruent sides.
![SQUARE Still has two pairs of parallel sides. Has four congruent sides Has four SQUARE Still has two pairs of parallel sides. Has four congruent sides Has four](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-15.jpg)
SQUARE Still has two pairs of parallel sides. Has four congruent sides Has four right angles
![A trapezoid has only one pair of parallel sides. A trapezoid has only one pair of parallel sides.](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-16.jpg)
A trapezoid has only one pair of parallel sides.
![An isosceles trapezoid is a trapeziod with the non-parallel sides congruent. An isosceles trapezoid is a trapeziod with the non-parallel sides congruent.](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-17.jpg)
An isosceles trapezoid is a trapeziod with the non-parallel sides congruent.
![TRAPEZOID has one pair of parallel sides. trapezoids Isosceles trapezoid (Each of these examples TRAPEZOID has one pair of parallel sides. trapezoids Isosceles trapezoid (Each of these examples](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-18.jpg)
TRAPEZOID has one pair of parallel sides. trapezoids Isosceles trapezoid (Each of these examples shown has top and bottom sides parallel. )
![An kite is a quadrilateral with NO parallel sides but 2 pairs of adjacent An kite is a quadrilateral with NO parallel sides but 2 pairs of adjacent](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-19.jpg)
An kite is a quadrilateral with NO parallel sides but 2 pairs of adjacent congruent sides.
![EXAMPLE OF A KITE 4 in. 2 in. EXAMPLE OF A KITE 4 in. 2 in.](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-20.jpg)
EXAMPLE OF A KITE 4 in. 2 in.
![](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-21.jpg)
![](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-22.jpg)
![CARNEGIE Homework: Read pg. 64 -65 pg. 66 # 7 -10, 13(!) CARNEGIE Homework: Read pg. 64 -65 pg. 66 # 7 -10, 13(!)](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-23.jpg)
CARNEGIE Homework: Read pg. 64 -65 pg. 66 # 7 -10, 13(!)
![TRAPEZOIDS AND KITES Chapter 5. 3 Homework: pg. 272 # 5, 6, 8, 9 TRAPEZOIDS AND KITES Chapter 5. 3 Homework: pg. 272 # 5, 6, 8, 9](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-24.jpg)
TRAPEZOIDS AND KITES Chapter 5. 3 Homework: pg. 272 # 5, 6, 8, 9
![ESSENTIAL QUESTIONS How do I use properties of trapezoids? How do I use properties ESSENTIAL QUESTIONS How do I use properties of trapezoids? How do I use properties](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-25.jpg)
ESSENTIAL QUESTIONS How do I use properties of trapezoids? How do I use properties of kites?
![VOCABULARY Trapezoid – a quadrilateral with exactly one pair of parallel sides. base leg VOCABULARY Trapezoid – a quadrilateral with exactly one pair of parallel sides. base leg](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-26.jpg)
VOCABULARY Trapezoid – a quadrilateral with exactly one pair of parallel sides. base leg base A trapezoid has two pairs of base angles. In this example the base angles are A & B and C & D
![5. 3 ISOSCELESTRAPEZOID CONJECTURE If a trapezoid is isosceles, then each pair of base 5. 3 ISOSCELESTRAPEZOID CONJECTURE If a trapezoid is isosceles, then each pair of base](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-27.jpg)
5. 3 ISOSCELESTRAPEZOID CONJECTURE If a trapezoid is isosceles, then each pair of base angles is congruent. A B, C D
![5. 3 ISOSCELESTRAPEZOID CONJECTURE CONVERSE If a trapezoid has a pair of congruent base 5. 3 ISOSCELESTRAPEZOID CONJECTURE CONVERSE If a trapezoid has a pair of congruent base](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-28.jpg)
5. 3 ISOSCELESTRAPEZOID CONJECTURE CONVERSE If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid. ABCD is an isosceles trapezoid
![8. 16 DIAGONALS OF A TRAPEZOID CONJECTURE A trapezoid is isosceles if and only 8. 16 DIAGONALS OF A TRAPEZOID CONJECTURE A trapezoid is isosceles if and only](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-29.jpg)
8. 16 DIAGONALS OF A TRAPEZOID CONJECTURE A trapezoid is isosceles if and only if its diagonals are congruent.
![EXAMPLE 1 PQRS is an isosceles trapezoid. Find m P, m Q and m EXAMPLE 1 PQRS is an isosceles trapezoid. Find m P, m Q and m](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-30.jpg)
EXAMPLE 1 PQRS is an isosceles trapezoid. Find m P, m Q and m R = 50 since base angles are congruent m P = 130 and m Q = 130 (consecutive angles of parallel lines cut by a transversal are )
![EX. 2: USING PROPERTIES OF TRAPEZOIDS Show that ABCD is a trapezoid. Compare the EX. 2: USING PROPERTIES OF TRAPEZOIDS Show that ABCD is a trapezoid. Compare the](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-31.jpg)
EX. 2: USING PROPERTIES OF TRAPEZOIDS Show that ABCD is a trapezoid. Compare the slopes of opposite sides. � The slope of AB = 5 – 0 = 5 = - 1 0 – 5 -5 � The slope of CD = 4 – 7 = -3 = - 1 7 – 4 3 The slopes of AB and CD are equal, so AB ║ CD. � The slope of BC = 7 – 5 = 2 = 1 4 – 0 4 2 � The slope of AD = 4 – 0 = 4 = 2 7 – 5 2 The slopes of BC and AD are not equal, so BC is not parallel to AD. So, because AB ║ CD and BC is not parallel to AD, ABCD is a trapezoid.
![DEFINITION Kite – a quadrilateral that has two pairs of consecutive congruent sides, but DEFINITION Kite – a quadrilateral that has two pairs of consecutive congruent sides, but](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-32.jpg)
DEFINITION Kite – a quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent.
![8. 19 THEOREM: OPPOSITE ANGLES OF A KITE If a quadrilateral is a kite, 8. 19 THEOREM: OPPOSITE ANGLES OF A KITE If a quadrilateral is a kite,](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-33.jpg)
8. 19 THEOREM: OPPOSITE ANGLES OF A KITE If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent A C, B D
![8. 18 THEOREM: PERPENDICULAR DIAGONALS OF A KITE If a quadrilateral is a kite, 8. 18 THEOREM: PERPENDICULAR DIAGONALS OF A KITE If a quadrilateral is a kite,](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-34.jpg)
8. 18 THEOREM: PERPENDICULAR DIAGONALS OF A KITE If a quadrilateral is a kite, then its diagonals are perpendicular.
![EXAMPLE 2 Find the side lengths of the kite. EXAMPLE 2 Find the side lengths of the kite.](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-35.jpg)
EXAMPLE 2 Find the side lengths of the kite.
![EXAMPLE 2 CONTINUED We can use the Pythagorean Theorem to find the side lengths. EXAMPLE 2 CONTINUED We can use the Pythagorean Theorem to find the side lengths.](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-36.jpg)
EXAMPLE 2 CONTINUED We can use the Pythagorean Theorem to find the side lengths. 122 + 202 = (WX)2 122 + 122 = (XY)2 144 + 400 = (WX)2 144 + 144 = (XY)2 544 = (WX)2 288 = (XY)2
![EXAMPLE 3 Find m G and m J. Since GHJK is a kite G EXAMPLE 3 Find m G and m J. Since GHJK is a kite G](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-37.jpg)
EXAMPLE 3 Find m G and m J. Since GHJK is a kite G J So 2(m G) + 132 + 60 = 360 2(m G) =168 m G = 84 and m J = 84
![TRY THIS! RSTU is a kite. Find m R, m S and m T. TRY THIS! RSTU is a kite. Find m R, m S and m T.](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-38.jpg)
TRY THIS! RSTU is a kite. Find m R, m S and m T. x +30 + 125 + x = 360 2 x + 280 = 360 2 x = 80 x = 40 So m R = 70 , m T = 40 and m S = 125
![EX. 4: USING THE DIAGONALS OF A KITE WXYZ is a kite so the EX. 4: USING THE DIAGONALS OF A KITE WXYZ is a kite so the](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-39.jpg)
EX. 4: USING THE DIAGONALS OF A KITE WXYZ is a kite so the diagonals are perpendicular. You can use the Pythagorean Theorem to find the side lengths. WX = √ 202 + 122 ≈ 23. 32 XY = √ 122 + 122 ≈ 16. 97 Because WXYZ is a kite, WZ = WX ≈ 23. 32, and ZY = XY ≈ 16. 97
![EX. 5: ANGLES OF A KITE Find m G and m J in the EX. 5: ANGLES OF A KITE Find m G and m J in the](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-40.jpg)
EX. 5: ANGLES OF A KITE Find m G and m J in the diagram at the 132° 60° right. SOLUTION: GHJK is a kite, so G ≅ J and m G = m J. 2(m G) + 132° + 60° = 360°Sum of measures of int. s of a quad. is 360° 2(m G) = 168°Simplify m G = 84° Divide each side by 2. So, m J = m G = 84°
![5. 4 PROPERTIES OF MIDSEGMENTS DEFINE AND DISCOVER PROPERTIES OF MIDSEGMENTS IN TRIANGLES AND 5. 4 PROPERTIES OF MIDSEGMENTS DEFINE AND DISCOVER PROPERTIES OF MIDSEGMENTS IN TRIANGLES AND](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-41.jpg)
5. 4 PROPERTIES OF MIDSEGMENTS DEFINE AND DISCOVER PROPERTIES OF MIDSEGMENTS IN TRIANGLES AND TRAPEZOIDS HOMEWORK Go over class notes, solve pg. 278 # 5, 6, 7
![](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-42.jpg)
![](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-43.jpg)
![HOMEWORK HOMEWORK](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-44.jpg)
HOMEWORK
![DEFINITION Midsegment of a trapezoid – the segment that connects the midpoints of the DEFINITION Midsegment of a trapezoid – the segment that connects the midpoints of the](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-45.jpg)
DEFINITION Midsegment of a trapezoid – the segment that connects the midpoints of the legs.
![MIDSEGMENT THEOREM FOR TRAPEZOIDS The midsegment of a trapezoid is parallel to each MIDSEGMENT THEOREM FOR TRAPEZOIDS The midsegment of a trapezoid is parallel to each](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-46.jpg)
MIDSEGMENT THEOREM FOR TRAPEZOIDS The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases.
![EX. 3: FINDING MIDSEGMENT LENGTHS OF TRAPEZOIDS LAYER CAKE A baker is making a EX. 3: FINDING MIDSEGMENT LENGTHS OF TRAPEZOIDS LAYER CAKE A baker is making a](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-47.jpg)
EX. 3: FINDING MIDSEGMENT LENGTHS OF TRAPEZOIDS LAYER CAKE A baker is making a cake like the one at the right. The top layer has a diameter of 8 inches and the bottom layer has a diameter of 20 inches. How big should the middle layer be?
![EX. 3: FINDING MIDSEGMENT LENGTHS OF TRAPEZOIDS E Use the midsegment theorem for trapezoids. EX. 3: FINDING MIDSEGMENT LENGTHS OF TRAPEZOIDS E Use the midsegment theorem for trapezoids.](http://slidetodoc.com/presentation_image/ecc5f2d8dd7502bed2bd4a29f567e312/image-48.jpg)
EX. 3: FINDING MIDSEGMENT LENGTHS OF TRAPEZOIDS E Use the midsegment theorem for trapezoids. DG = ½(EF + CH)= ½ (8 + 20) = 14” D C F G D
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