1. 6-2 Properties of Parallelograms
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Objective: To relate sides, angles, diagonals, and transversals of parallelograms THEOREM 6-1 Opposite sides of a parallelogram are congruent

2. CONSECUTIVE ANGLES: angles of a polygon that share a side Ex: Find m S in RSWT. R and S are consecutive angles of a parallelogram. They are supplementary (S.S.I.A) m R + m S = m S = 180 m S = 68 R S
112° T W

3. Opposite angles of a parallelogram are congruent
THEOREM 6-2
Opposite angles of a parallelogram are congruent
Find the value of y in EFGH. Then find m E, m G,
m F, and m H F G
3y + 37°
6y + 4° E H
6y + 4 = 3y + 37
3y + 4 = 37
So, E = 6• = 70° = G
3y = 33
Then, F = 180 – 70 = 110 = H
y = 11

4. The diagonals of a parallelogram bisect each other
THEOREM 6–3
The diagonals of a parallelogram bisect each other
Proof of THEOREM 6-3
Given: ABCD
Prove: AC and BD bisect
each other at E
Statements Reasons
ABCD is a parallelogram ) Given
AB // DC ) Definition of a parallelogram
1 = 4, 2 = ) Alt. interior ‘s are =
AB = DC ) Opposite sides of a are =
ABE = CDE ) ASA
AE = CE, BE = DE ) CPCTC
AC and BD bisect each ) Definition of bisector
other at E B C 2 4 E 1 3 A D

5. THEOREM 6-4 If three (or more) parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal BD = DF A B C D E F

6. A B
P Parallelogram ABCD
D C
If AB = 3x + 11
BC = 2x + 19
CD = 7x – 17 Find x
If m BAD = y and m ADC = 4y – 70, find y
If m ABC = 2x and m ADC = 6x + 84, find m BCD
3x + 11= 7x – 17
x = 7
y + 4y – 70 = 180
y = 50
2x = 6x + 84
x = 4, Angle ABC = 108, and Angle BCD = 72

7. Assignment:
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