Question

right triangle abc is isosceles and point m is the midpoint of the hypotenuse.
what is true about triangle amb?
it is congruent to triangle abc.
it is an obtuse triangle.
it is an isosceles right triangle.
it is a scalene triangle.

Explanation:

Step1: Identify triangle ABC properties

Right isosceles triangle ABC has right angle at B, so AB=BC, ∠ABC=90°. Hypotenuse is AC.

Step2: Midpoint M of hypotenuse

In right triangle, midpoint of hypotenuse is equidistant from all vertices: AM=BM=CM.

Step3: Check triangle AMB

AB=BC, M is midpoint, so AM=BM. ∠AMB: Since ∠ABC=90°, and BM=AM=CM, ∠ABM=∠BAM=45°, so ∠AMB=90°. Thus AMB is isosceles right triangle.

Answer:

It is an isosceles right triangle.