Question

From the following figure, we can say: $AD=CE$

State TRUE or FALSE

• A. True
• B. False

Answer 1

The correct option is A True

In $△$ ABC,
$AB=AC$
thus, $\angle ABC=\angle ACB=x$ (Opposite angles of equal sides are equal)
Now, $\angle ABC+\angle CBE=180$ (Angles on a straight line)
$x+\angle CBE=180$
$\angle CBE=180-x$ (I)
Also, $\angle ACB+\angle ACD=180$ (Angles on a straight line)
$x+\angle ACD=180$
$\angle ACD=180-x$ (II)
Hence, from I and II
$\angle ACD=\angle CBE$
In triangles ACD and CBE
$\angle ACD=\angle CBE$
$CD=CB$ (Given)
$AC=BE$ (Given)
Thus, $△ACD\cong △ECB$
Hence, $AD=CE$