Question

Given QT = SR, QV = SU, and the diagram, prove that triangles QUT and SVR are congruent. Write a paragraph proof.

Answer 1

Answer:

Triangles QUT and SVR are congruent because the defining two sides and an included angle of triangles QUT and SVR are equal

Step-by-step explanation:

Here we have QT = SR and

QV = SU

Therefore,

QT = √(UT² + QU²)........(1)

RS = √(VS² + RV²)..........(2)

Since QS = QU + SU = QV + VS ∴ QU = VS

Therefore, since SR = QT and QU = VS, then from (1) and (2), we have UT = RV

Hence since we know all sides of the triangles QUT and SVR are equal and we know that the angle in between two congruent sides of the the triangles QUT and SVR that is the angle in between sides QU and UT for triangle QUT and the angle in between the sides RV and VS in triangle SVR are both equal to 90°, therefore triangles QUT and SVR are congruent.