HW—pg. 433 (14-25, 27-32)
Ch. 6 Test WED 1-14, p. 4 & THU 1-15, p. 2
www.westex.org HS, Teacher Website
1-12-15
Warm up—Geometry H
1. Use the diagonals to determine whether a parallelogram with vertices A(3, 7), B(2, 1),
C(-4, 2), and D(-3, 8) is a rectangle, rhombus, or square. Give all names that apply.
Distance formula (length of diagonals)
AC = BD =
Slope formula ( diagonals) neg. rec. slope
AC m = BD m =
Today’s Goal
I will be able to:
1. use properties of kites to solve problems.
2. use properties of trapezoids to solve problems.
HW—pg. 433 (14-25, 27-32)
Ch. 6 Test WED 1-14, p. 4 & THU 1-15, p. 2
www.westex.org HS, Teacher Website
Name ______Date ______
Geometry H
6.6 Properties of Kites and Trapezoids
Today’s Goal
I will be able to:
1. use properties of kites to solve problems.
2. use properties of trapezoids to solve problems.
A ______is a quadrilateral with exactly two pairs of congruent consecutive sides.
Example 1: Using Properties of Kites
In kite ABCD, mÐDAB = 54°, and mÐCDF = 52°.
a. Find mÐBCD. b. Find mÐABC. c. Find mÐFDA.
YOU TRY:
In kite PQRS, mÐPQR = 78°, and mÐTRS = 59°.
a. Find mÐQRT. b. Find mÐQPS. c. Find mÐPSR.
A ______ is a quadrilateral with exactly one pair of parallel sides. Each of the parallel sides is called a ______. The nonparallel sides are called ______. ______of a trapezoid are two consecutive angles whose common side is a base.
If the legs of a trapezoid are congruent, the trapezoid is an ______. The following theorems state the properties of an isosceles trapezoid.
Example 2: Using Properties of Isosceles Trapezoids
a. Find mÐA.
b. KB = 21.9m and MF = 32.7. Find FB.
YOU TRY:
a. Find mÐF.
b. JN = 10.6, and NL = 14.8. Find KM.
Example 3: Applying Conditions for Isosceles Trapezoids
a. Find the value of a so that PQRS is isosceles.
b. AD = 12x – 11, and BC = 9x – 2. Find the value of x so that ABCD is isosceles.
YOU TRY:
Find the value of x so that PQST is isosceles.
The ______ is the segment whose endpoints are the midpoints of the legs. In Lesson 5-1, you studied the Triangle Midsegment Theorem. The Trapezoid Midsegment Theorem is similar to it.
Example 4: Finding Lengths Using Midsegments
Find EF.
YOU TRY:
Find EH.
6.6 Practice
In kite HJKL, mÐKLP = 72°, and mÐHJP = 49.5°. Find each measure.
1. mÐLHJ 2. mÐPKL
Use the diagram for Items 3 and 4.
3. mÐWZY = 61°. Find mÐWXY.
4. XV = 4.6, and WY = 14.2. Find VZ.
5. Find LP.
EXIT TICKET Name ______
What is one thing you know is true about an isosceles trapezoid?
EXIT TICKET Name ______
What is one thing you know is true about an isosceles trapezoid?
EXIT TICKET Name ______
What is one thing you know is true about an isosceles trapezoid?
EXIT TICKET Name ______
What is one thing you know is true about an isosceles trapezoid?