Q12 of 47 Page 7

ABCD is a square, X and Y are points on sides AD and BC respectively such that AY = BX. Prove that BY = AX and ∠BAY = ∠ABX.

Given that ABCD is a square, X and Y are points on the sides AD and BC respectively.

Such that,


AY = BX


To prove: BY = AX and ∠BAY = ∠ABX


Proof:



Join B and X, A and Y


Since, ABCD is a square


∠DAB = ∠CBA = 90o


∠XAB = ∠YBA = 90o (i)


Now, consider


We have,


∠XAB = ∠YBA = 90o [From (i)]


BX = AY (Given)


AB = BA (Common side)


So, by RHS congruence rule, we have



(By c.p.c.t)



More from this chapter

All 47 →
10

PQR is a triangle in which PQ = PR and S is any point on the side PQ. Through S, a line is drawn parallel to QR and intersecting PR at T. Prove that PS = PT.

 1

ABC is a triangle and D is the mid-point of BC. The perpendicular from D to AB and AC are equal. Prove that the triangle is isosceles.

 13

In Δ ABC, if ∠A=40° and ∠B=60° . Determine the longest and shortest sides of the triangle.

 14

In Δ ABC, ∠B=35 o, ∠C=65 o and the bisector of ∠ABC meets BC in P. Arrange AP, BP and CP in descending order.