# PARALLELOGRAM PROPERTIES WORKSHEET

Parallelogram Properties Worksheet :

Worksheet given in this section is much useful to the students who would like to practice problems on properties of parallelograms.

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## Parallelogram Properties Worksheet - Problems

Problem 1 :

Find the lengths of SR and SK in the parallelogram shown below. Explain your reasoning.

Problem 2 :

Find the measures of ∠C and ∠B in the parallelogram ABCD.

Problem 3 :

Find the value of x in the parallelogram ABCD shown below.

Problem 4 :

In the diagram shown below, ABCD and AEFG are parallelograms. Prove that m∠1  ≅  m∠3.

Problem 5 :

In the parallelogram ABCD shown below, prove that WX  ≅  YZ and WZ  ≅  XY.

## Parallelogram Properties Worksheet - Solutions

Problem 1 :

Find the lengths of SR and SK in the parallelogram shown below. Explain your reasoning.

Solution :

Finding the length of SR :

By Theorem, opposite sides of a parallelogram are congruent.

So, we have

SR  =  PQ

From the diagram, PQ  =  5.

SR  =  5

Finding the length of SK :

By Theorem, diagonals of a parallelogram bisect each other.

So, we have

SK  =  QK

From the diagram, QK  =  3.

SK  =  3

Problem 2 :

Find the measures of ∠C and ∠B in the parallelogram ABCD.

Solution :

Finding the measure of ∠C :

By Theorem, opposite angles of a parallelogram are congruent.

So, we have

m∠C  =  m∠A

From the diagram, m∠A  =  70°.

m∠C  =  70°

Finding the measure of ∠B :

By Theorem, consecutive  angles of a parallelogram are supplementary.

So, we have

m∠A  +  m∠B  =  180°

From the diagram, m∠A  =  70°.

70°  +  m∠B  =  180°

Subtract 70° from both sides.

m∠B  =  110°

Problem 3 :

Find the value of x in the parallelogram ABCD shown below.

Solution :

By Theorem, consecutive  angles of a parallelogram are supplementary.

So, we have

m∠D  +  m∠C  =  180°

Substitute m∠D  =  3x° and m∠C  =  120°.

3x°  +  120°  =  180°

Subtract 120° from both sides.

3x°  =  60°

3x  =  60

Divide both sides by 3.

x  =  20

Problem 4 :

In the diagram shown below, ABCD and AEFG are parallelograms. Prove that m∠1  ≅  m∠3.

Solution :

Plan : Show that both angles are congruent to m∠2. Then use the Transitive Property of Congruence.

 Statements ABCD is a parallelogram AEFG is a parallelogramaaaaa m∠1  ≅  m∠2 aaa aaaaa m∠2  ≅  m∠3 aaam∠1  ≅  m∠2 Reasonsaaaaaaaaa Given aaaaaaa aaaaaaaaaaaaaaaaaaaaaaaOpposite angles of a parallelogram are congruent. Transitive property of congruence.

Problem 5 :

In the parallelogram ABCD shown below, prove that WX  ≅  YZ and WZ  ≅  XY.

 Statements aaaaaa WXYZ is a aaaaa aaaa parallelogram aaaaaaaaaa Draw XZ aaaaaa aaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaWX || YZ, WZ || XY aa m∠WXZ  ≅  m∠YZX a aa m∠WZX  ≅  m∠YXZ aaaaaa ZX  ≅  ZX aaaaa aaaaaaaaaaaaaaaaaaaaaΔWZX  ≅  ΔYXZ  WX  ≅  YZ, WZ  ≅  XY Reasonsaaaaaaaaaa Given aaaaaaaaa  aaaaaaaaaaaaaaaaaaaaaaaaaaThrough any two points  there exists exactly one a aaaaaaaaa line.Definition of parallelogramAlternate Interior Angles TheoremReflexive Property of CongruenceASA Congruence PostulateCorresponding parts of congruent triangles are congruent

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