Question

In $△ A BC$ and $△ PQR$ , AD and PS are altitudes such that $△ A B D \sim △ PQS$ and $△ A C D \sim △ PRS$ . Prove that $△ A BC \sim △ PQR$ .

Approach

Given the similarities, by CPCT we have $A C = A B$ and $A D = A E$ . This gives $\frac{A B}{A D} = \frac{A C}{A E}$ and $∠ A$ is common. By SAS similarity criterion, $△ A D E \sim △ A BC$ .

Step-by-step working

1
From given similarities: $A C = A B$ , $A D = A E$
1 mark
2
By SAS similarity: $△ A D E \sim △ A BC$
1 mark

Concepts used

similaritytrianglesaltitudescpct

Approach

Step-by-step working

Concepts used

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