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

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

Step-by-step 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 .

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step-by-step explanation:

answer: about 22.67

step-by-step explanation: