Question

In the figure given below, $∠1 = ∠2$ and $\frac{BE}{BC} = \frac{C D}{A B}$ . Prove that $△ B D E \sim △ B A C$ .

Approach

Given $∠1 = ∠2$ implies $B D = C D$ . From given ratio and substitution $\frac{BE}{BC} = \frac{B D}{A B}$ . With $∠ B$ common, by SAS similarity criterion, $△ B D E \sim △ B A C$ .

Step-by-step working

1
$∠1 = ∠2 \Rightarrow B D = C D$
0.5 marks
2
Given: $\frac{BE}{BC} = \frac{C D}{A B} = \frac{B D}{A B}$
0.5 marks
3
$∠ B$ common, by SAS: $△ B D E \sim △ B A C$
1 mark

Concepts used

similaritysas criteriontrianglesproof

Approach

Step-by-step working

Concepts used

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