1. Bell Ringer 2. 3. 1.

2. Properties of Parallelograms

3. Parallelogram
Parallelogram – is a quadrilateral with both pairs of opposite sides parallel.

4. Find Side Lengths of Parallelograms
Example 1
Find Side Lengths of Parallelograms
FGHJ is a parallelogram. Find JH and FJ.
SOLUTION
JH = FG
Opposite sides of a are congruent.
Substitute 5 for FG.
= 5
FJ = GH
Opposite sides of a are congruent.
Substitute 3 for GH.
= 3
ANSWER
In FGHJ, JH = 5 and FJ = 3. 4

5. Now You Try  Find Side Lengths of Parallelograms
ABCD is a parallelogram.
Find AB and AD. 1.
ANSWER
AB = 9; AD = 8

6. Find Angle Measures of Parallelograms
Example 2
Find Angle Measures of Parallelograms
PQRS is a parallelogram. Find
the missing angle measures.
SOLUTION
By Theorem 6.3, the opposite angles of a parallelogram are congruent, so mR = mP = 70°. 1. 2.
By Theorem 6.4, the consecutive angles of a parallelogram are supplementary.
Consecutive angles of a are supplementary.
mQ + mP = 180°
Substitute 70° for mP.
mQ + 70° = 180°
Subtract 70° from each side.
mQ = 110° 6

7. Example 2
Find Angle Measures of Parallelograms
By Theorem 6.3, the opposite angles of a parallelogram are congruent, so mS = mQ = 110°. 3.
ANSWER
The measure of R is 70°, the measure of Q is 110°, and the measure of S is 110°. 7

8. Now You Try  mB = 120° mC = 60° mD = 120° ANSWER mA = 75°
Find Angle Measures of Parallelograms
ABCD is a parallelogram. Find the missing angle measures. 2.
ANSWER
mB = 120°
mC = 60°
mD = 120°
ANSWER
mA = 75°
mB = 105°
mC = 75° 3.

9. Find Segment Lengths Diagonals of a bisect each other.
Example 3
Find Segment Lengths
TUVW is a parallelogram.
Find TX.
SOLUTION
TX = XV
Diagonals of a bisect each other.
Substitute 3 for XV.
= 3 9

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