Question

Match the following STATEMENTS to the reasons listed.

NOTE: In a traditional proof format, the statements would be on the left side of the proof.

Given:
RM = SN
TM = TN
Prove:
RN = SM

1. RM = SN, TM = TN Addition Property of Equality
2. ∠T = ∠T Reflexive
3. RM + TM = SN + TN Substitution
4. RM + TM = RT, SN + TN = ST Betweeness
5. RT = ST CPCTE
6. Triangle RTN congruent to Triangle STM Given
7. RN = SM SAS

Answer 1

We have to match the following statements to the given proof.

S.No. Proof Statement

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1 RM=SN Given

TM=TN

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2 ∠T=∠T Reflexive

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3 RM+TM=SN+TN Addition property

of equality

( by using 1)

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4 RM+TM=RT, Betweeness

SN+TN=ST

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5 RT=ST Substitution( since using

equation 3 and 4)

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6 ΔRTN≅ΔSTM SAS ( since two sides and

corresponding angle are

equal by 1,2 and 5)

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7 RN=SM CPCTE( Corresponding parts of

congruent triangles are equal)

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Answer 2

We are given with RM = SN, TM = TN and we are to prove that RN = SM. The steps that are followed for this proof are as follow:


1. RM = SN , TM = TN Given
2. ∠T = ∠T Reflexive
3. RM + TM = SN + TN Addition Property of Equality
4. RM + TM = RT, SN + TN = ST Betweeness
5. RT = ST Substitution
6. Triangle RTN congruent to Triangle STM SAS
7. RN = SM CPCTE