1. Ways to Prove That Quadrilaterals are Parallelograms
Chapter 5 Section 2
Ways to Prove That Quadrilaterals are Parallelograms

2. Warm-Up: Tuesday April 1
Get your homework out to be checked from last night.
Solve the following quadratics using ANY method of your choice! Today you may give decimal approximations for your answers.

3. Homework Answers: April 1
1.) CR, CE 2.) REC, WCE, WEC 3.) ER, RC, CW 4.) CRW, CWR, EWR 5.) a = 8, b = 10, x = 118, y = 62 6.) a = 8, b = 15, x =80, y = 70 7.) a = 5, b = 3, x = 120, y = 22 8.) a = 9, b = 11, x = 33, y = 27 9.) a = 8, b = 8, x = 56, y = ) a = 10, b = 4, x = 90, y = ) ) ST = 14, SP = 13
Homework Answers: April 1
p. 169 #’s 1 – 12, 19-28

4. 19. ) x=3, y=5 20. ) x=7, y=18 21. ) x=13, y=5 22. ) x=65, y=20 23
19.) x=3, y=5 20.) x=7, y=18 21.) x=13, y=5 22.) x=65, y=20 23.) x=5, y=4 24.) x=10, y=16 25.) 5,2 26.) 6,3,42 27.) 10,70 28.) 36,49
p. 169 #’s 1 – 12, 19-28

6. 22.)
85
130
x - y
x + y

7. Proving Quadrilaterals Are Parallelograms
Remember all the properties of parallel lines?
What about congruent triangles?

8. What do Parallel Lines Make?
Congruent Corresponding Angles
Congruent Alternate Interior Angles
Supplementary Same Side Interior Angles
Remember… FUZZ!!
122

9. Recall… Ways to Prove Triangles Congruent
Side-Side-Side
Side-Angle-Side
Angle-Side-Angle
Angle-Angle-Side
Hypotenuse Leg
Use CPCTC to state corresponding angles or sides are congruent.

10. What Are We Trying To Do Again?
We want to prove that any quadrilateral is a parallelogram.
GOAL: (use properties from Chapter 3)
Get back to the definition of a parallelogram:
A parallelogram is a quadrilateral with both pairs of opposite sides parallel.

11. Theorem 5.4:
If both pairs of opposite sides of a quadrilateral are , then the quadrilateral is a parallelogram.
What would we need to show that ABCD is a parallelogram?
congruent A D C B

12. Statements Reasons Proof of Theorem 5.4 Given: TS  QR; TQ  SR
Prove: Quad QRST is a parallelogram Q R
Statements
Reasons

13. Theorem 5.5: congruent parallel
If one pair of opposite sides of a quadrilateral are both and , then the quadrilateral is a parallelogram.
What would we need to show that ABCD is a parallelogram?
congruent
parallel A D C B

14. Statements Reasons Proof of Theorem 5.5 Given: AB  CD; AB || CD
Prove: Quad ABCD is a parallelogram D C
Statements
Reasons

15. Theorem 5.6:
If both pairs of opposite angles of a quadrilateral are , then the quadrilateral is a parallelogram.
What would we need to show that ABCD is a parallelogram?
congruent A D C B

16. Statements Reasons Proof of Theorem 5.6 Given: mA = mC = xB
Given: mA = mC = x
mB = mD = y
Prove: Quad ABCD is a parallelogram D C
Statements
Reasons

17. Theorem 5.7: diagonals bisect
If the of a quadrilateral each other, then the quadrilateral is a parallelogram.
What would we need to show that WXYZ is a parallelogram?
diagonals
bisect W Z Y X

18. Class Practice Look at the marking on each figure
and decide if each quadrilateral
must be a parallelogram. If the
answer is yes, state the definition
or property that applies.

19. Both pairs of opposite sides are congruent!
Is it a Parallelogram? 14 6
YES
Both pairs of opposite sides are congruent!

20. Is it a Parallelogram? 4 YES One pair of opposite sides are both
parallel and congruent!

21. The diagonals bisect each other!
Is it a Parallelogram?
YES
The diagonals bisect each other!

22. None of the properties are satisfied!
Is it a Parallelogram?
105 70
NO!
None of the properties are satisfied!

23. Consecutive Angles are Supplementary!
Is it a Parallelogram?
YES
Consecutive Angles are Supplementary!

24. Is it a Parallelogram? 3 YES One pair of opposite sides are both
parallel and congruent!

25. p. 173 Classroom Exercises #’s 1 - 11
Practice Exercises
p. 173 Classroom Exercises #’s

26. Cool Down: Wednesday, March 26th
Summarize the 5 ways to prove parallelograms
1.)
2.)
3.)
4.)
5.)
Solve for x and y. y2 x
3x - 40
Y + 30
Cool Down Part 1
Cool Down Part 2

27. Statements Reasons A X C B F E D Given: ABCX is a parallelogram
DXFE is a parallelogram
Prove: B  E
Statements
Reasons