Trapezoids and Kites

Geometry

http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.5%20Trapezoids.ppt

Objective, DFA, HW

 Objective: SWBAT verify & use properties of trapezoids & kites.

 DFA: p.338-341 # 14  HW - p.338-341 (2-50 even)

Using properties of trapezoids

 A trapezoid is a quadrilateral with exactly one pair of parallel sides.  The parallel sides are the

bases

. leg D A base base B leg C http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.5%20Trapezoids.ppt

Using properties of trapezoids

 A trapezoid has two pairs of

base angles

. For instance in trapezoid ABCD  D and  C are one pair of base angles. The other pair is  A and  B. leg D  The nonparallel sides are the

legs

trapezoid. of the A base base B leg C http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.5%20Trapezoids.ppt

Using properties of trapezoids

 If the legs of a trapezoid are congruent, then the trapezoid is an isosceles trapezoid.

http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.5%20Trapezoids.ppt

Trapezoid Theorems

Theorem 9-16   If a trapezoid is isosceles, then each pair of base angles is congruent.

 A ≅  B,  C ≅  D D A B C http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.5%20Trapezoids.ppt

Trapezoid Theorems

Theorem 9-17  A trapezoid is isosceles if and only if its diagonals are congruent.

 ABCD is isosceles if and only if AC ≅ BD.

D A B http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.5%20Trapezoids.ppt

C

Ex: Using properties of Isosceles Trapezoids   PQRS is an isosceles trapezoid. Find m  P, m  Q, m  R.

m RQ = 2.16 cm m PS = 2.16 cm PQRS is an isosceles trapezoid, so m  R = m  S = 50 °. Because  S and  P are consecutive interior angles formed by parallel lines, they are supplementary. So m  P = 180 °- 50° = 130°, and m  Q = m  P = 130° S 50 ° P Q You could also add 50 and 50, get 100 and subtract it from 360 ° . This would leave you 260/2 or 130 ° .

R http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.5%20Trapezoids.ppt

Using properties of kites

 A kite is a quadrilateral that has two pairs of

consecutive

congruent sides, but opposite sides are not congruent. http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.5%20Trapezoids.ppt

Kite theorems

Theorem 9-18   If a quadrilateral is a kite, then its diagonals are perpendicular.

AC  BD B A C http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.5%20Trapezoids.ppt

D

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.

W WX = √20 2 XY = √12 2 + 12 + 12 2 2 ≈ 23.32

≈ 16.97

Because WXYZ is a kite, WZ = WX ≈ 23.32, and ZY = XY ≈ 16.97

X 20 12 12 U 12 Z Y http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.5%20Trapezoids.ppt

Venn Diagram:

http://teachers2.wcs.edu/high/rhs/staceyh/Geometry/Chapter%206%20Notes.ppt#435,22,6.2 – Properties of Parallelograms

Flow Chart:

http://www.quia.com/pop/103618.html?AP_rand=172732766

Properties of Quadrilaterals

 http://www.quia.com/pop/103618.html?A

P_rand=172732766