Maths-
General
Easy

Question

In the figure, ray AZ bisects straight angle D A B as well as straight angle D C B.
(i) State the three pairs of equal parts in triangles BAC and DAC.
(ii) Is ΔBAC ⩭ ΔDAC ? Give reasons.
(iii) Is AB = AD? Justify your answer.
(iv) Is CD = CB? Give reasons.

hintHint:

First find the congruence rule and then proceed.

The correct answer is: 2 different triangles.


    (i) From the figure, we have
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell straight angle D A C equals straight angle B A C end cell row cell straight angle D C A equals straight angle B C A end cell end table
    AC = AC (common side)
    (ii) By, ASA congruence criterion, the triangles are congruent.
    That is, straight angle D A C equals straight angle B A C
    straight angle D C A equals straight angle B C A
    AC = AC
    (iii) Since the triangles are congruent, AB = AD because both sides originate from
    equal angles in 2 different triangles.
    (iv) Since the triangles are congruent, CD = CB because both sides originate from
    equal angles in 2 different triangles.

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