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: Recall property of isosceles right - triangle

In an isosceles right - triangle \(ABC\) with \(\angle B = 90^{\circ}\) and \(AB=BC\), and \(M\) is the mid - point of the hypotenuse \(AC\). The median drawn to the hypotenuse of a right - triangle is half the length of the hypotenuse. So \(AM = BM=CM\).

Step2: Analyze angles

Since \(\triangle ABC\) is isosceles right - triangle, \(\angle A=\angle C = 45^{\circ}\). Also, \(AM = BM\), so \(\angle A=\angle ABM = 45^{\circ}\), then \(\angle AMB=90^{\circ}\).

Step3: Determine the type of \(\triangle AMB\)

Since \(AM = BM\) and \(\angle AMB = 90^{\circ}\), \(\triangle AMB\) is an isosceles right - triangle.

Answer:

It is an isosceles right triangle.