Download presentation
Presentation is loading. Please wait.
Published bySamuel Lindsey Modified over 9 years ago
1
Trapezoids and Kites Chapter 8, Section 5 (8.5)
2
Essential Questions How do I use properties of trapezoids?
How do I use properties of kites?
3
Vocabulary Trapezoid – a quadrilateral with exactly one pair of parallel sides. A trapezoid has two pairs of base angles. In this example the base angles are A & B and C & D leg base
4
8.14 Base Angles Trapezoid Theorem
If a trapezoid is isosceles, then each pair of base angles is congruent. A B, C D
5
8.15 Base Angles Trapezoid Converse
If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid. ABCD is an isosceles trapezoid
6
8.16 Diagonals of a Trapezoid Theorem
A trapezoid is isosceles if and only if its diagonals are congruent.
7
Example 1 PQRS is an isosceles trapezoid. Find m P, m Q and mR.
m R = 50 since base angles are congruent mP = 130 and mQ = 130 (consecutive angles of parallel lines cut by a transversal are )
8
Definition Midsegment of a trapezoid – the segment that connects the midpoints of the legs.
9
8.17 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.
10
Definition Kite – a quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent.
11
8.18 Theorem: Perpendicular Diagonals of a Kite
If a quadrilateral is a kite, then its diagonals are perpendicular.
12
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
13
Example 2 Find the side lengths of the kite.
14
Example 2 Continued We can use the Pythagorean Theorem to find the side lengths. = (WX)2 = (WX)2 544 = (WX)2 = (XY)2 = (XY)2 288 = (XY)2
15
Example 3 Find mG and mJ. Since GHJK is a kite G J
So 2(mG) + 132 + 60 = 360 2(mG) =168 mG = 84 and mJ = 84
16
Try This! RSTU is a kite. Find mR, mS and mT.
x x = 360 2x = 360 2x = 80 x = 40 So mR = 70, mT = 40 and mS = 125
17
Homework Pages 546 (7-15)
Similar presentations
© 2024 SlidePlayer.com. Inc.
All rights reserved.