Question

ΔABC is a right triangle, right angled at B.BP is perpendicular to AC and PQ is perpendicular to BC. The triangles $△$ABC,$△$
APB, \ (\triangle\)PBQ, Δ\ (\triangle\)PQC, Δ$△$ BPC are all similar.

• A. True
• B. False

Answer 1

The correct option is A

True

Consider :

∠BAP = ∠BAC [common angle]

∠BPA = ∠ABC [90°]

By AA similarity criterion, $△$ABP ~ $△$ACB -------------------------- 1

Similarly, we can show that $△$BPC ~ $△$ACB -------------------------- 2

Now Consider :

∠PBQ = ∠PBC [common angle]

∠BQP = ∠BPC [90°]

By AA similarity criterion, $△$BPQ ~ $△$BCP --------------------------- 3

Similarly, we can show that $△$PQC ~ $△$BPC --------------------------- 4

From 1,2,3,4, we can infer that the triangles $△$ACB,$△$ABP, $△$BPQ, $△$PQC, $△$BPC are all similar. Hence, True.