ProofModerate1 mark
6(b)
In the given figure AB = 9 cm, PA = 7.5 cm and PC = 5 cm. [3] Chords AD and BC intersect at P.
Prove that ΔPAB ΔPCD
Topic: Similarity / scale factor
Previous-year question practice database
Answer
Exam answer
Given:
AB = 9 cm PA = 7.5 cm PC = 5 cm
In triangles PAB and PCD:
∠APB = ∠CPD because they are vertically opposite angles.
Also:
∠ABP = ∠PDC
Both are angles at the circumference standing on the same chord AC.
Therefore:
ΔPAB ∼ ΔPCD by the AA similarity criterion.
Hence proved.
Explanation
The two triangles have one pair of vertically opposite angles at P and a second equal-angle pair standing on the same chord AC. Two equal angle pairs are sufficient to prove similarity by AA.
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