PARALLELOGRAM PROPERTIES WORKSHEET

About "Parallelograms 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 parallelogram

aaaaa m∠1  ≅  m∠2 aaa aaaaa m∠2  ≅  m∠3 aaa

m∠1  ≅  m∠2

Reasons

aaaaaaaaa Given aaaaaaa aaaaaaaaaaaaaaaaaaaaaaa

Opposite 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 aaaa

aaaaaa Draw XZ aaaaaa aaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa

WX || YZ, WZ || XY 

aa m∠WXZ  ≅  m∠YZX a aa m∠WZX  ≅  m∠YXZ

aaaaaa ZX  ≅  ZX aaaaa aaaaaaaaaaaaaaaaaaaaa

ΔWZX  ≅  ΔYXZ

  WX  ≅  YZ, WZ  ≅  XY

Reasons

aaaaaaaaaa Given aaaaaaaaa  aaaaaaaaaaaaaaaaaaaaaaaa

aaThrough any two points  there exists exactly one a aaaaaaaaa line.

Definition of parallelogram

Alternate Interior Angles Theorem

Reflexive Property of Congruence

ASA Congruence Postulate

Corresponding parts of congruent triangles are congruent

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