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Question

In given figure, EBAC, BGAE and CFAE Prove that:

(i) ΔABGΔDCB
(ii) BCBD=BEBA

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Solution



Given: EBAC, BGAE and CFAE

To prove: (i) ΔABGΔDCB

(ii) BCBD=BEBA

Proof: (i) In ΔABG and ΔDCB, BG||CF as corresponding angles are equal.

2=7=5 [Each 90]

6=4 [Corresponding angles]

ΔABGΔDCB

[By AA similarity]
1=3 [CPST]
(ii) In ΔABE and ΔDBC
1=3 [Proved above]
ABE=5
[Each is 90, EBAC (Given)]
ΔABEΔDBC [By AA similarity]
In similar triangles, corresponding sides are proportional
ABBD=BEBC
BCBD=BEBA

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