PROVING STATEMENTS ABOUT ANGLES WORKSHEET

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

1. Answer :

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

Transitive property of equality

Definition of congruent angles

2. Answer :

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

3. Answer :

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

4. Answer :

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

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PROVING STATEMENTS ABOUT ANGLES WORKSHEET

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