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