PROVING STATEMENTS ABOUT SEGMENTS AND ANGLES WORKSHEET

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

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.

1. Answer :

2. Answer :

Given : LK = 5, JK = 5, JK ≅ JL

Prove : LK ≅ JL

A.  LK = 5

B.  JK = 5

C.  Definition of congruence segments

D.  LK ≅ JL

3. Answer :

Given : Q is the midpoint of PR

Prove : PQ = 1/2 ⋅ PR and QR = 1/2 ⋅ PR.

4. 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

5. Answer :

6. Answer :

7. Answer :

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