# Ex.6.3 Q8 Triangles Solution - NCERT Maths Class 10

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## Question

$$E$$ is a point on the side $$AD$$ produced of a parallelogram $$ABCD$$ and $$BE$$ intersects $$CD$$ at $$F.$$ Show that $$\Delta \text{ }ABE\text{ }\sim{\ }\text{ }\Delta CFB.$$

Diagram

## Text Solution

Reasoning:

If two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar.

This may be referred to as the $$AA$$ similarity criterion for two triangles.

Steps:

In $$\Delta \rm{A B E}, \Delta \rm{C F B}$$

$$\angle B A E=\angle F C B$$ (opposite angles of a parallelogram)

$$\angle A E B=\angle F B C$$  [$$\because$$ AE || BC  and  EB is a transversal alternate angle]

$$\Rightarrow\qquad \Delta ABE \sim \Delta C F E$$ ($$AA$$criterion)

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