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 a scalene triangle. it is an isosceles right triangle.

Explanation:

• In an isosceles right - triangle \(ABC\) (\(\angle B = 90^{\circ}\), \(AB=BC\)), the mid - point \(M\) of the hypotenuse \(AC\) has the property that \(AM = BM\) (by the property of the mid - point of the hypotenuse of a right - triangle: the mid - point of the hypotenuse of a right - triangle is equidistant from the three vertices).
• Also, \(\angle AMB=90^{\circ}\) (since the line from the mid - point of the hypotenuse of a right - triangle to the right - angled vertex is perpendicular to the hypotenuse in an isosceles right - triangle).

Answer:

It is an isosceles right triangle.