Prove the congruence of the three pairs of the sides of â–³ SRT and â–³ QRT.
Statements
Reasons
1.
SR≅ QR
1.
Given
2.
ST≅ TQ
2.
Definition of midpoint
3.
RT≅ RT
3.
Reflexive Property of Congruence
4.
△ SRT≅ △ QRT
4.
SSS Theorem
Practice makes perfect
We are given that SR≅ QR. This means that segments SR and QR have equal measures. Let's add this piece of information to the diagram.
This is going to be the first step of the proof.
1) SR≅ QR
1) Given
Now, let's use the fact that T is a midpoint of SQ. By the definition of a midpoint, segments ST and TQ are congruent and have the same measure.
2) ST≅ TQ
2) Definition of midpoint
From the diagram, we can also see that both △ SRT and △ QRT share side RT. Using the Reflexive Property of Congruence, which states that any geometric figure is congruent to itself, we get that RT ≅ RT.
3) RT≅ RT
3) Reflexive Property of Congruence
Now that we proved the congruence of all three pairs of the sides of the triangles â–³ SRT and â–³ QRT, by the SSS Theorem we conclude that â–³ SRT is congruent to â–³ QRT.
4) △ SRT≅ △ QRT
4) SSS Theorem
Let's use these steps to write a two-column proof.
