Question

what is the missing reason in the proof? statements reasons 1. sp ≅ sr 1. given 2. st ⊥ pr 2. converse of the perpendicular bisector theorem 3. pt ≅ rt 3. ? 4. qt ⊥ pr 4. st and qt name the same line. 5. qp ≅ qr 5. perpendicular bisector theorem 6. δqpt ≅ δqrt 6. hl theorem definition of perpendicular bisector definition of congruence reflexive property substitution property

Answer 1

The missing reason in the congruency proof given the parameters is; Definition of a perpendicular bisector.

How to prove congruency theorems?

We are given;

Triangle QPT is similar to triangle QRT.

SP ≅ SR

Now, According to perpendicular bisector definition, we know that perpendicular bisector is a line or a segment that is perpendicular to a segment and passes through the midpoint of the segment. This means that any point on the perpendicular bisector is equidistant from the endpoints of the line segment.

Thus, we can say that PT ≅ RT and the missing reason is definition of a perpendicular bisector.

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