CK-12 Geometry-Concepts

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

Given:ABCDis a parallelogram with diagonalBD

Prove:AB∼=DC,AD∼=BC

TABLE6.4:

Statement Reason

1.ABCDis a parallelogram with diagonalBD Given

2.AB||DC,AD||BC Definition of a parallelogram

3.^6 ABD∼=BDC,^6 ADB∼=DBC Alternate Interior Angles Theorem
4.DB∼=DB Reflexive PoC
5. 4 ABD∼= 4 CDB ASA
6.AB∼=DC,AD∼=BC CPCTC

Example A

ABCDis a parallelogram. Ifm^6 A= 56 ◦, find the measure of the other three angles.

Draw a picture. When labeling the vertices, the letters are listed, in order, clockwise.

Ifm^6 A= 56 ◦, thenm^6 C= 56 ◦because they are opposite angles.^6 Band^6 Dare consecutive angles with^6 A, so
they are both supplementary to^6 A.m^6 A+m^6 B= 180 ◦, 56 ◦+m^6 B= 180 ◦,m^6 B= 124 ◦.m^6 D= 124 ◦.

Example B

Find the values ofxandy.

Opposite sides are congruent, so we can set each pair equal to each other and solve both equations.

6 x− 7 = 2 x+ 9 y^2 + 3 = 12

4 x= 16 y^2 = 9

x= 4 y= 3 or− 3

Even thoughy=3 or -3, lengths cannot be negative, soy=3.