Question

IF YOU TOLD CORRECT I WILL MARK YOU AS BRAINLIST​

Answer 1

Required Answer:-

The line segment XY of ∆XBY is parallel to the side AC of ∆ABC, Then prove that ∆ABC ~ ∆XBY

Here,

XY and AC are parallel to each other. Hence there will be a pair of corresponding angles at corners of A & B and X & Y in both triangles$.$

• ∠ABC = ∠XBY (Common)
• ∠BXY = ∠BAC (Corresponding angles)

Hence,

• ∆ABC ~ ∆XBY (By AA similarity)

$\therefore$ Hence, Proved!!

Note:-

• You can choose ∠BYX and ∠BCA as the corresponding angle pair as well.
• Just we have to prove any two angles to be equal in measure for proving the similarity by AA criterion.

Answer 2

GIVEN :

The line segment XY of ∆XBY is parallel to the side AC of ∆ABC, Then prove that ∆ABC ~ ∆XBY

HERE,

XY and AC are parallel to each other.

Hence, there will be a pair of corresponding angles at corners of A & B and X & Y in both triangles....

• ∠ABC = ∠XBY (Common)
• ∠BXY = ∠BAC (Corresponding angles)

HENCE,

∆ABC ~ ∆XBY (By AAS congruence rule )

→ HENCE, Proved