6-2 Properties of Parallelograms

6-2 Properties of Parallelograms

What is a parallelogram?

Quadrilateral with both pairs of opposite sides parallel (PROPERTY #1).

In a quadrilateral, opposite sides do not share a vertex and opposite angles do not share a side.

If a quadrilateral is a parallelogram, then its opposite sides are congruent.

Theorem 6-3 (PROPERTY #2)

Multiple Choice

The figure is a parallelogram.  
Solve for x.  

• 1
• 11
• 7
• 6

Consecutive Angles

If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.

m∠A + m∠B = 180° m∠A + m∠D = 180°
m∠D + m∠C = 180° m∠C + m∠B = 180°

Theorem 6-4 (PROPERTY #3)

• Angles of a polygon that share a side

What are they?

Multiple Select

Which properties of parallelograms have we learned this far?

• Opposite sides are congruent

• Opposite sides are parallel

• Consecutive angles are supplementary

• Consecutive angles are complementary

Multiple Choice

In a parallelogram, consecutive angles are __________.

• congruent

• supplementary

• corresponding

• parallel

Multiple Choice

Find the m∠R.

• 40°

• 140°

• 50°

• 180°

Multiple Choice

The figure is a parallelogram.

Solve for x.

• 1

• 10

• 4

• 5

Fill in the Blank

The figure is a parallelogram.  
Solve for x.  

If a quadrilateral is a parallelogram, then its opposite anlges are congruent.

Theorem 6-5 (PROPERTY #4)

Multiple Choice

Find the value of a.

• 38

• 114

• 3

• 74

Fill in the Blank

Find the value of a.

Multiple Choice

Find the value of a.

• 65

• 30

• 15

• 45

​Statements	​Reasons
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Proof Practice

1. Opposite sides are parallel (2 sets)

2. Opposite sides are congruent (2 sets)

Review - Properties we have learned so far....

3. Consecutive angles are supplementary

4. Opposite angles are congruent (2 sets)

If a quadrilateral is a parallelogram, then its diagonals bisect each other.

Theorem 6-6 (PROPERTY #5)

Multiple Choice

The figure to the left is a parallelogram. Find the value of f.

• -5
• 15
• 5
• 20

Multiple Choice

Find the value of j and k.

• j = 4.5, k = 2

• j = 4.5, k = 5

• j = 3, k = 10

• j = 5, k = 5

Fill in the Blank

If EF=FG=GH=6 and AD =15, what is CD?

Open Ended

Exit Ticket: State the 5 properties of a parallelogram we have learned in this lesson.