Question

Manvi made decorative pieces for children of orphanage which had two isosceles triangle with common base. prove that line joining their vertics bisects common base at right angle

Answer 1

In triangles ABD and ACD,
AB = AC (sides of isosceles triangle)
Similarly, BD = DC
AD = AD (common)
therefore triangle ABD is congruent to ACD (by SSS)
Therefore angles BAO = CAO (by cpct).

In triangles ABO and ACO,
AB = AC
AO = AO (common)
angles BAO = CAO (proved above)
Therefore, triangle ABO is congruent to ACO (by SAS).
Therefore , angles AOB = AOC (by cpct)
Also, BO = CO (by cpct)

also, Angles AOB + AOC = 180° (by linear pair)
so, 2AOB =180° i.e. AOB = 90°

Hence,AD bisect BC perpendicularly and BO = CO.

Hope it helps!

Answer 2

Answer:

above answer is absolutely correct