ABC and DBC are two isosceles triangles on the same base BC (see Fig. 7.33). Show that ∠ ABD = ∠ ACD

Question

ABC and DBC are two isosceles triangles on the same base BC (see Fig. 7.33). Show that &#x2220; ABD = &#x2220; ACD

Philoid · Accepted Answer

It is given in the question that ABC and DBC are two isosceles triangles

To show: ∠ABD = ∠ACD

Proof: Let us join AD, as shown in the figure:

In, ΔABD and ΔACD

AD is the common side

AB = AC (ABC is an isosceles triangle)

BD = CD (BCD is an isosceles triangle)

Therefore,

By Side-Side-Side Congruency,

ΔABD ≅ ΔACD

Thus,

∠ABD = ∠ACD (By Corresponding Parts of Congruent Triangles)