PROVING STATEMENTS ABOUT ANGLES WORKSHEET
About "Proving statements about angles worksheet"
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.
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 - Solution
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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