**Proving statements about angles worksheet :**

Worksheet given in this section is much useful to the students who would like to practice problems on Properties of Angle Congruence.

**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

**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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