Question

1. given

△wux ≅ △vux
by sas congruence conditions and
ux is a ⊥ bisector of △wuv
and
m∠wuv = 90°
what is true about
△wuv?

triangle wuv is an acute triangle

triangle wuv is an isosceles right triangle

triangle wuv is a right triangle

triangle wuv is an equilateral triangle

Explanation:

1. First, we know that \( m\angle WUV = 90^\circ \), so \( \triangle WUV \) is a right triangle.
2. Given \( \triangle WUX \cong \triangle VUX \) by SAS, this implies \( WU = VU \) (corresponding parts of congruent triangles are congruent).
3. A right triangle with two equal sides (legs) is an isosceles right triangle. An acute triangle has all angles less than \( 90^\circ \), which is not the case here. An equilateral triangle has all sides equal and all angles \( 60^\circ \), which also does not match. Just saying it's a right triangle is less specific than identifying it as an isosceles right triangle since we also know two sides are equal.

Answer:

B. Triangle WUV is an isosceles right triangle