Given: Vertical isosceles triangles. RS bisects QT. ∠R ≅ ∠S.
Prove: ∆QRP ≅ ∆TSP
2 paragraph proof
so how would I format this?
like any of the other similar proofs in your text. State what is given and what can be deduced using known properties.
looks like ASA again. Vertical angles are congruent.
To prove that ∆QRP is congruent to ∆TSP, we can use the Angle-Angle-Side (AAS) congruence criterion.
First, we know that RS bisects QT. This means that RS divides QT into two equal parts. Therefore, QR and TS are congruent as they are opposite sides of the bisection.
Next, we are given that ∠R is congruent to ∠S. Since we have a vertical isosceles triangle, the base angles are equal. Therefore, ∠R is congruent to ∠Q and ∠S is congruent to ∠T.
Now, we have the following congruences:
∠R ≅ ∠S (given)
∠Q ≅ ∠R (isosceles triangle property)
∠S ≅ ∠T (isosceles triangle property)
QR ≅ TS (as RS bisects QT)
By using Angle-Angle-Side (AAS) congruence, we have enough information to conclude that ∆QRP is congruent to ∆TSP. Therefore, the proof is complete.