CBSE Class 10 Maths (Basic) 2024 · Paper 430/3/1 · Question 30

Triangles 3 marks Hard

In the given figure,

∠ A B C = ∠ A C B

and

\frac{B C}{B E} = \frac{B D}{A C}

. Show that

△ A B E \sim △ D B C

and

A E ∥ D C

Triangle DBC with A on DB and E on BC

Answer

△ A B E \sim △ D B C

by SAS similarity (common

∠ B

and

\frac{B A}{B D} = \frac{B E}{B C}

, using

A B = A C

), with

A \leftrightarrow D

B \leftrightarrow B

E \leftrightarrow C

. Hence

∠ B A E = ∠ B D C

, and these corresponding angles give

A E ∥ D C

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