Question

In the figure below, WU ≅ VT.

Square W V U T has point Y in the middle. Lines are drawn from each point of the square to the opposite point to form 4 triangles. Angle W T U and T U V are right angles.

The
congruency theorem can be used to prove that △WUT ≅ △VTU.

Answer 1

Use the Hypotenuse–Leg (HL) congruence theorem (also called RHS for right triangles).

Proof sketch:
- ∠WTU and ∠TUV are right angles, so △WUT and △VTU are right triangles.
- WU ≅ VT (given) — these are the hypotenuses.
- TU is common to both triangles, so TU ≅ TU (a leg).

Thus by HL, △WUT ≅ △VTU.