Question

Match the reasons with the statements in the proof to prove ∠RNT = ∠SMT given RT = ST and MT = NT

Given: RT = ST MT = NT

To Prove: ∠RNT = ∠SMT


1. RT = ST MT = NT

2. ∠T = ∠T

3. RNT = STM SAS

4. ∠RNT = ∠SMT


Reflexive Property

Given

SAS (Side-Angle-Side)

CPCTE (Corresponding Parts of Congruent Triangles are Equal)

Answer 1

1. given

2. Reflexive Property

3. SAS (Side-Angle-Side)

4. CPCTE (Corresponding Parts of Congruent Triangles are Equal)

Answer 2

See explanation

Explanation:

1. RT=ST, MT=NT -given

2. ∠T=∠T - reflexive property (angle T in triangle RNT is congruent to angle T in triangle SMT)

3. ΔRNT=ΔSMT - SAS (two sides and included angle in triangle RNT are congruent to two sides and included angle in triangle SMT)

4. ∠RNT=∠SMT - CPCTE (Corresponding Parts of Congruent Triangles are Equal)

The reflexive property of equality simply states that a value is equal to itself.

SAS: Triangles are congruent if any pair of corresponding sides and their included angles are equal in both triangles.