Missing Sides of Parallelograms

6-2 PROPERTIES OF
PARALLELOGRAMS

OBJECTIVE

•To use the properties of sides, angles, diagonals,
and transversals in quadrilaterals to find
missing values, side and diagonal lengths,
and angle measures.

PROPERTIES: SIDES AND ANGLES
•Theorem 6-1

PROPERTIES: SIDES AND ANGLES

• CONSECUTIVE ANGLES of a parallelogram are

SUPPLEMENTARY.

• Consecutive angles are angles that share a SIDE.

Open Ended

Name the 4 pairs of consecutive angles in parallelogram ABCD.

PROPERTIES: SIDES AND ANGLES

• Theorem 6-2

PROPERTIES: SIDES AND ANGLES

• Example 2

Fill in the Blanks

PROPERTIES: DIAGONALS AND
TRANSVERSALS

• Theorem 6-3

• The DIAGONALS of parallelograms BISECT each

other.

Draw

Draw on the parallelogram to show that they bisect each other.

PROPERTIES: DIAGONALS AND
TRANSVERSALS

• Example 3

• Remember: To solve a system, ISOLATE one

variable. Then, SUBSTITUTE into the other to
solve.

Open Ended

What system would you make for this parallelogram?

PROPERTIES: DIAGONALS AND
TRANSVERSALS

• 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.

Fill in the Blanks

Multiple Choice

The figure is a parallelogram.  
Solve for x.  

• 1
• 11
• 7
• 6

Multiple Choice

The figure is a parallelogram.  
Solve for x.  

• 7
• 1
• 5
• 2

Multiple Choice

The figure is a parallelogram.  
Solve for x.  

• 1
• 10
• 4
• 5

Multiple Choice

The figure is a parallelogram.  
Solve for x.  

• 0
• 6
• 5
• 9