Question

Complete the proof that RS ≅ PQ.

Answer 1

below!

Explanation:

reasons for each of the statements.

1. this is given information so there is nothing to prove here.

2. this is also given information, nothing to prove here.

3. this is also given information, nothing to prove here.

4. This is just because they are both 2 parts of the big segment (not sure what exactly is the reason your question is looking for but it something along these lines should be in your dropdown menu).

5. same as 4

6. since QR is equal to TU you can substitute TU with QR. QT stays the same.

7. Since we can see based on 5 and 6 that they have the same values by the same equations.

8. SAA

9. CPCTC

Hope this was helpful! :)

Answer 2

We need to prove triangles are PQU and SRT are congruent and we can see they have two angles marked as congruent and the included sides partially marked as equal and include the common segment.

We'll first prove the sides RT and QU are congruent, then prove the triangles are congruent. It will then give us the corresponding sides' congruence.

Missing reasons:

• 1. Given
• 2. Given
• 3. Given

The first 3 statements reflect the given fact.

• 4. Segment addition
• 5. Segment addition

The next 2 statements reflect segment addition postulate.

• 6. Substitution property of equality
• 7. Transitive property of equality

After substitution of equal segments we prove that partially overlapping sides are congruent. Then it gives us the missing bit to prove the congruence of triangles.

• 8. ASA congruence

Corresponding Parts of Congruent Triangles are Congruent.

• 9. CPCTC