Question

In the figure, ACD and ECB are straight lines and EF || AD. If

angle FEC = 2 angle CAB, prove that triangle ABC is an isosceles triangle.​

Answer 1

#See details below

Explanation:

#An isosceles triangle has two equal angles:
`\angle FEC=2\angleCAB\\\\\angle FEC=\angle DCB \ \ \ \ \ \#Co-alternate \ angles\\\\\angle ACB= 180 -\angle DCB\ \ \ \ \ \#angles \ on \ a \ straight \ line\\\\\angle CAB=180-\angle ACB=\angle CBA`

#An isosceles triangle has two equal sides;

Using sine rule:

`(a)/(sin \ A)=(b)/(sin \ B)\\\\(ac)/(sin B)=(cb)/(sin A) \ \ \ \ \ \ \ \ \ \ \ \ #\angle CAB=\angle CBA\\\\\therefore ac=cb`

Now, given that ABC has two equal sides and two equal triangle it is an isosceles triangle.