Match the following columns.


Column I



Column II



(a)In ∆ABC, if AB=AC and ∠A=50°, then ∠C=…………….



(p) its perimeter



(b) The vertical angle of an isosceles triangle is 130°. Then, each base angle is…….



(q) 15°



(c) The sum of three altitudes of a ∆ABC is less than…………



(r) 65°



(d) In the given figure, ABCD is a square and ∆EDC is an equilateral triangle. Then, ∠EBC is………….




(s) 25°



The correct answer is:


(A)-………, (B)-………, (C)-…….., (D)-……..,

The parts of the question are solved below:

a. Given: In △ABC, AB = AC and ∠A=50°


Thus, ∠B = ∠C


Now, ∠A + ∠B + ∠C = 180° (The angle sum property of triangle)


50 + 2∠B = 180°


2∠B = 130°


∠C = ∠B = 65°


b. As per the question,


Let the vertical angle be A and ∠ B = ∠ C


Now, ∠A + ∠B + ∠C = 180° (The angle sum property of triangle)


130 + 2∠B = 180°


2∠B = 50°


∠C = ∠B = 25°


c. We know that, the sum of three altitudes of a triangle ABC is less than its perimeter.


d. Here, ABCD is a square and EDC is a equilateral triangle.


∴ ED = CD = AB = BC = AD = EC


In ΔECB,


EC = BC


∠C = ∠B = x


∠ECD = 60° and ∠DCB = 90°


∠ECB = 60° + 90°


= 150°


Now, x + x + 150° = 180°


2x = 30°


x = 15°


∴∠EBC = 15°


∴ a = r, b = s, c = p, d = q


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