Geometry

5.2 Ways to Prove that Quadrilaterals are Parallelograms

There are 5 Ways to Prove that a Quadrilateral is a THE FIRST WAY. We already know the first

one, by the defn. of that…

1) Both pairs of opp. sides //

Parallelogram

or

Defn. of

THE SECOND WAY (Theorem)

2) Both pairs of opp. sides =~

Parallelogram

THE THIRD WAY (Theorem)

3) One pair of opp. sides both // and =~

Parallelogram

THE FOURTH WAY (Theorem)

4) Both pairs of opp. ‘s =~

Parallelogram

7

THE FIFTH WAY (Theorem)

5) Diagonals bisect each other

Parallelogram

The Five Ways to Show a Quadrilateral is a Parallelogram

2) Both pairs of opp. sides =~

3) One pair of opp. sides both // and =~

4) Both pairs of opp. ‘s =~

7

5) Diagonals bisect each other

1) Defn. of

PG 173 CE

1. 2. 3.

4. 5. 6.

7. 8. 9.

10. 11. 12.

(2x – 5)

3y

1233y – 8

x2 y + 12

2x + 15

7y3x

4y + 2145

|| ;

;

ogramWXYZ

MZ WN NY WN

||MNYZ is a ogram

|| ogramWXYZ

||WN ZY

;MZ WN NY WN

||MZ NY

||MNYZ is a ogram

W

Z

M X N

Y

Given:

Prove:

1. 1.

2. 2.

3. 3.

4. 4.

5. 5.

REVIEW: Angle Bisector Theorem for problem #15

HW

P. 174 (1-10, 14, 19-22)

P. 384 (17)

Canned foods

One from the HW

P. 174 #6 Has two possible answers