CK-12 Geometry Concepts

6.6. Trapezoids http://www.ck12.org

Guided Practice

T RAPan isosceles trapezoid.

Find:

1.m^6 T PA

2.m^6 PT R

3.m^6 PZA

4.m^6 ZRA

Answers:

1.^6 T PZ∼=^6 RAZsom^6 T PA= 20 ◦+ 35 ◦= 55 ◦.
2.^6 T PAis supplementary with^6 PT R, som^6 PT R= 125 ◦.
3. By the Triangle Sum Theorem, 35◦+ 35 ◦+m^6 PZA= 180 ◦, som^6 PZA= 110 ◦.
4. Sincem^6 PZA= 110 ◦,m^6 RZA= 70 ◦because they form a linear pair. By the Triangle Sum Theorem,m^6 ZRA=
90 ◦.

Practice

1. Can the parallel sides of a trapezoid be congruent? Why or why not?

For questions 2-7, find the length of the midsegment or missing side.

2.

3.

4.

5.

6.

7.

Find the value of the missing variable(s).

8.

Find the lengths of the diagonals of the trapezoids below to determine if it is isosceles.

9.A(− 3 , 2 ),B( 1 , 3 ),C( 3 ,− 1 ),D(− 4 ,− 2 )

10.A(− 3 , 3 ),B( 2 ,− 2 ),C(− 6 ,− 6 ),D(− 7 , 1 )

11.A( 1 , 3 ),B( 4 , 0 ),C( 2 ,− 4 ),D(− 3 , 1 )

12.A( 1 , 3 ),B( 3 , 1 ),C( 2 ,− 4 ),D(− 3 , 1 )

13. Write a two-column proof of the Isosceles Trapezoid Diagonals Theorem using congruent triangles.

Given:T RAPis an isosceles trapezoid withT R||AP.

Prove:T A∼=RP

14. How are the opposite angles in an isosceles trapezoid related?.


15. List all the properties of a trapezoid.