511. In ∆ABC and ∆DEF, if AB = DF, BC = DE, AC = EF and ∆D = 55°. Then, ∠B =

• 55°
• 35°
• 90°
• 90°

In the following figure, ∠B = ∠D = 90° and BC = CD. Then, the relation between AB and DE is

• AB = DE  
• AB > DE
• AB < DE 
• AB < DE 
• AB < DE 

 In ∆ABC, AB = AC, BD = EC. Then, ∆ADE is

• right angled
• scalene
• isosceles
• isosceles

Show that ΔABC, where A(–2, 0), B(2, 0), C(0, 2) and ΔPQR where P(–4, 0), Q(4, 0), R(0, 2) are similar triangles. 

Given $∆ABC ~ ∆PQR, if \frac{AB}{PQ} = \frac{1}{3}, then find \frac{ar∆ABC}{ar∆PQR}$

Prove that the area of an equilateral triangle described on one side of the square is equal to half the area of the equilateral triangle described on one of its diagonal.

If the area of two similar triangles are equal, prove that they are congruent.

In an equilateral △ABC, is a point on side BC such that BD =1/3BC. Prove that 9 (AD)² = 7(AB)²

Prove that, in a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.

ABCD is a rectangle whose three vertices are B (4, 0), C(4,3) and D(0, 3). The length of one of its diagonals is

• 5

• 4

• 3

• 25