Maths-
General
Easy

Question

In the figure, ABC is an isosceles triangle with AB = AC. If D is the midpoint of BC, prove that:
(i) ΔABD⩭ ΔACD
(ii) straight angle A D C equals straight angle A D B equals90°

hintHint:

Find the congruence rule and from that find the angles.

The correct answer is: 90°


    (i) In ΔABD and ΔACD, we have
    AB = AC (isosceles triangle)
    AD = AD (common side)
    BD = DC (Since D is the midpoint of BC)
    Hence ΔABD⩭  ΔACD by SSS congruence rule.
    (ii) Since  ΔABD⩭  ΔACD by SSS congruence rule
    We have, straight angle ADC equals straight angle ADB
    straight angle ADC plus straight angle ADB equals 180 to the power of ring operator (linear pair)
    therefore straight angle ADC equals straight angle ADB equals 180 over 2 equals 90 to the power of ring operator

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