Proving Statements about Segments and Angles Worksheet :
Worksheet given in this section will be much useful for the students who would like to practice problems on proving statements about segments and angles.
Problem 1 :
In the diagram given above, PQ ≅ XY. Prove XY ≅ PQ
Problem 2 :
Use the diagram and the given information to complete the missing steps and reasons in the proof.
Given : LK = 5, JK = 5, JK ≅ JL
Prove : LK ≅ JL
Statements A B LK = JK LK ≅ JK JK ≅ JL D |
Reasons Given Given Transitive property of equality C Given Transitive property of congruence |
Problem 3 :
In the diagram given below, Q is the midpoint of PR.
Show that PQ and QR are each equal to 1/2 ⋅ PR.
Problem 4 :
Prove the Transitive Property of Congruence for angles.
Problem 5 :
In the diagram shown below,
m∠3 = 40°, ∠1 ≅ ∠2, ∠2 ≅ ∠3
Prove m∠1 = 40°
Problem 6 :
In the diagram shown below,
∠1 and ∠2 are right angles
Prove ∠1 ≅ ∠2
Problem 7 :
In the diagram shown below,
∠1 and ∠2 are supplements,
∠3 and ∠4 are supplements,
∠1 ≅ ∠4
Prove ∠2 ≅ ∠3
Problem 1 :
In the diagram given above, PQ ≅ XY. Prove XY ≅ PQ
Solution :
Statements PQ ≅ XY PQ = XY XY = PQ XY ≅ PQ |
Reasons Given Definition of congruence statements Symmetric property of equality Definition of congruence segments |
Problem 2 :
Use the diagram and the given information to complete the missing steps and reasons in the proof.
Given : LK = 5, JK = 5, JK ≅ JL
Prove : LK ≅ JL
Statements A B LK = JK LK ≅ JK JK ≅ JL D |
Reasons Given Given Transitive property of equality C Given Transitive property of congruence |
Solution :
A. LK = 5
B. JK = 5
C. Definition of congruence segments
D. LK ≅ JL
Problem 3 :
In the diagram given below, Q is the midpoint of PR.
Show that PQ and QR are each equal to 1/2 ⋅ PR.
Solution :
Given : Q is the midpoint of PR
Prove : PQ = 1/2 ⋅ PR and QR = 1/2 ⋅ PR
Statements aaaa Q is the aaa aamidpoint of PR PQ = QR PQ + QR = PR PQ + PQ = PR 2 ⋅ PQ = PR PQ = 1/2 ⋅ PR QR = 1/2 ⋅ PR |
Reasons Given aaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaa Definition of midpoint Segment Addition Postulate Substitution property of equality Distributive property Division property of equality Substitution property of equality |
Problem 4 :
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 5 :
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 6 :
In the diagram shown below,
∠1 and ∠2 are right angles
Prove ∠1 ≅ ∠2
Solution :
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 7 :
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 segments and angles.
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