Question

Right triangle ABC is isosceles and point M is the midpoint oh the hypotenuse. What is true about triangle AMB?

(A) congruent to triangle ABC
(B) obtuse triangle
(C) isosceles right triangle
(D) scalene triangle

Answer 1

I just did that one, it's C - isosceles right triangle.

Answer 2

Answer: Option C) is true about ΔAMB . It is an isosceles right triangle.

Explanation:

Given : Right triangle ABC is isosceles and point M is the midpoint on the hypotenuse AC.

Construct a line joining B and M

In triangle AMB and triangle CMB

AM=MC [ as M is the mid point of AC]

∠BAM=∠BCM ..................(1)

AB=BC

∴ΔAMB=ΔCMB [by SAS criteria of congruence]

⇒∠AMB=∠CMB [CPCTC] .....................(2)

Now ∠AMB+∠CMB =180° [linear pair]

⇒∠AMB+∠AMB=180° [from (2)]

⇒∠AMB=90°

In triangle ABC and triangle AMB

∠A=∠BAM

∠B=∠AMB=90°

⇒ΔABC≈ΔAMB [by AA similarity criteria]

⇒ΔAMB is an isosceles right triangle .