Question

Complete the two-column proof.

Given:
RT = RU
TS = US

Prove:
△RST ≅ △RSU



Statement Reason
1. RT = RU; TS = US 1. Given
2. RS = RS ?
3. △AMD ≅ △BMC 3. SSS
Which of the following options best completes reason #2 in the triangle congruency proof?

vertical angles are equal
symmetric property of equality
reflexive property of equality
distributive property of equality

Answer 1

reflexive property of equality.

Answer 2

2. RS=RS

Reason : Reflexive property of equality.

Explanation:

Given RT=RU

TS=US

To prove that
`\triangle RST \cong \triangle RSU`

Proof:

1. Statement: RT=RU; TS= US

Reason: Given in question

2.Statement: RS=RS

Reason: Reflexive property of equality.

Reflexive property: It is that property of equality which define a relation with itself.

3. Statement:
`\triangle AMD \cong \triangle BMC`

Reason: SSS ( Side -SIde -Side congruence property of triangles)

Hence proved.

The correct answer is reflexive property of equality .