PROVING STATEMENTS ABOUT ANGLES WORKSHEET

Proving Statements About Angles Worksheet :

Worksheet given in this section will be much useful for the students who would like to practice problems proving statements about angles.

Proving Statements About Angles Worksheet - Problems

Problem 1 :

Prove the Transitive Property of Congruence for angles.

Problem 2 :

In the diagram shown below,

m∠3 = 40°, ∠1 ≅ ∠2, ∠2 ≅ ∠3

Prove m∠1 = 40° Problem 3 :

In the diagram shown below,

∠1 and ∠2 are right angles

Prove ∠1 ≅ ∠2 Problem 4 :

In the diagram shown below,

∠1 and ∠2 are supplements,

∠3 and ∠4 are supplements,

∠1 ≅ ∠4

Prove ∠2 ≅ ∠3  Proving Statements About Angles Worksheet - Solutions

Problem 1 :

Prove the Transitive Property of Congruence for angles.

Solution :

To prove the Transitive Property of Congruence for angles, begin by drawing three congruent angles.

Label the vertices as A, B and C. Given :

∠A ≅ ∠B

∠B ≅ ∠C

Prove :

∠A ≅ ∠C

Statements

∠A ≅ ∠B, ∠B ≅ ∠C

m∠A = m∠B

m∠B = m∠C

m∠A = m∠C

∠A ≅ ∠C

Reasons

Given

Definition of congruent angles

Definition of congruent angles

Transitive property of equality

Definition of congruent angles

Problem 2 :

In the diagram shown below,

m∠3 = 40°, ∠1 ≅ ∠2, ∠2 ≅ ∠3

Prove m∠1 = 40° Solution :

Statements

m∠3 = 40°

∠1 ≅ ∠2

∠2 ≅ ∠3

∠1 ≅ ∠3

m∠1 = m∠3

m∠1 = 40°

Reasons

Given

Transitive Property of Congruence

Definition of congruent angles

Substitution property of equality

Problem 3 :

In the diagram shown below,

∠1 and ∠2 are right angles

Prove ∠1 ≅ ∠2 Statements

aaaa ∠1 and ∠2 are aa aaaaa right angles

m∠1 = 90°,  m∠2 = 90°

m∠1 = m∠2

∠1 ≅ ∠2

Reasons

Given aaaaaaaaaaaaaaaaaaaaa aaaaaaaaa

Definition of right angle

Transitive property of equality

Definition of congruent angles

Problem 4 :

In the diagram shown below,

∠1 and ∠2 are supplements,

∠3 and ∠4 are supplements,

∠1 ≅ ∠4

Prove ∠2 ≅ ∠3 Statements

∠1 and ∠2 are supplements

∠3 and ∠4 are supplements

∠1 ≅ ∠4

m∠1 + m∠2 = 180°   m∠3 + m∠4 = 180°

m∠1  =  m∠4

a ∠1 + ∠2 = ∠3 + ∠1 aaaaaa

m∠2 = m∠3

∠2 ≅ ∠3

Reasons

aaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaa

Given aaaaaaaaaaaaaaaaaaaaaa aaaaaa

Definition of Supplementary angles aaaaaaaaaaaaaaaaaaaa

Definition of congruent angles

Substitution property of equality aaaaaaaaaaaaaaaaaa

Subtraction property of equality

Definition of congruent angles After having gone through the stuff given above, we hope that the students would have understood how to prove statements about angles

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