Question
ABCD is a cyclic quadrilateral AB and DC are produced to meet in E. Prove that Δ EBC ∼ Δ EDA.
✓
Answer
In Δ EBC and Δ EDA, we have
∠ EBC = ∠ EDA ...[ Exterior or angle in a cyclic quadrilateral is equal to opposite interior angle]∠ ECB = ∠ EAD ...[ Exterior or angle in a cyclic quadrilateral is equal to opposite interior angle]
and ∠ E = ∠ E
So, by AAA exterior of similarly, we get
Δ EBC ∼ Δ EDA
Hence proved.
∠ EBC = ∠ EDA ...[ Exterior or angle in a cyclic quadrilateral is equal to opposite interior angle]∠ ECB = ∠ EAD ...[ Exterior or angle in a cyclic quadrilateral is equal to opposite interior angle]
and ∠ E = ∠ E
So, by AAA exterior of similarly, we get
Δ EBC ∼ Δ EDA
Hence proved.
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