Question

Name the third pair of corresponding part so that triangle AOC is congruent to triangle BOD, If O is the midpoint of AB and angle A = angle B by ASA congruence? ​

Answer 1

In triangle AOC and triangle BOD

we have,

Angle CAO = Angle OBD (given)

Side OA = Side OB (as O is the mid point of AB)

Angle AOC = Angle BOD (by vertically opposite angle of triangle are equal).

Therefore triangle AOC congruent to triangle BOD ( by ASA)

therefore AC = BD (by c.p.c.t)

and AC is parallel to BD ( Angle CAO = Angle DBO)

But these two angle are alternate interior angle therefore AC is parallel to BD.

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