CK-12 Geometry Concepts

http://www.ck12.org Chapter 6. Polygons and Quadrilaterals

3.m^6 D= 72 ◦as well, because opposite angles are congruent.^6 Aand^6 Care supplementary with^6 D, som^6 A=
m^6 C= 108 ◦.

Practice

1. Ifm^6 S= 143 ◦in parallelogramPQRS, find the other three angles.


2. IfAB⊥BCin parallelogramABCD, find the measure of all four angles.


3. Ifm^6 F=x◦in parallelogramEF GH, find expressions for the other three angles in terms ofx.

For questions 4-11, find the measures of the variable(s). All the figures below are parallelograms.

4.

5.

6.

7.

8.

9.

10.

11.

Use the parallelogramWAV Eto find:

12.m^6 AW E

13.m^6 ESV

14.m^6 W EA

15.m^6 AV W

In the parallelogramSNOW,ST= 6 ,NW= 4 ,m^6 OSW= 36 ◦,m^6 SNW= 58 ◦andm^6 NT S= 80 ◦. (diagram is not
drawn to scale)

16.SO

17.NT

18.m^6 NW S

19.m^6 SOW

Plot the pointsE(− 1 , 3 ),F( 3 , 4 ),G( 5 ,− 1 ),H( 1 ,− 2 )and use parallelogramEF GHfor problems 20-23.

20. Find the coordinates of the point at which the diagonals intersect. How did you do this?


21. Find the slopes of all four sides. What do you notice?


22. Use the distance formula to find the lengths of all four sides. What do you notice?


23. Make a conjecture about how you might determine whether a quadrilateral in the coordinate is a parallelogram.

Write a two-column proof.

24.Opposite Angles Theorem

25.

26.Given

27. :
    28.ABCD