# Ex.7.2 Q5 Triangles Solution - NCERT Maths Class 9

## Question

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

## Text Solution

**What is Known?**

\(ABC\) and \(DBC\) are two isosceles triangles.

**To prove:**

\(\angle \text{ABD}=\angle \text{ACD}\)

**Reasoning:**

First of all, we can join point \(A\) and \(D\) then we can show two triangles \(ADB\) and \(ADC\) congruent by using SSS congruency rule after that we can say corresponding parts of congruent triangles will be equal.

**Steps:**

Let us join \(AD.\)

In \(\triangle ABD \text { and } \Delta ACD,\)

\[\begin{align}&AB = AC\;( \text {Given} ) \\ &BD = CD( \text {Given} )\\ &AD = AD \; (\text{Common side}) \\& \therefore \Delta ABD \cong \Delta ACD \\&(\text{By SSS congruence rule}) \end{align}\]

\[\begin{align}&\therefore \Delta ABD = \Delta ACD \;(\text{By }CPCT) \end{align}\]