Math the following columns:
Column I | Column II |
(a)In ∆ABC, if AB=AC and ∠A=70°, then ∠C=……….. | (p) less |
(b) The vertical angle of an isosceles triangle is 120°. Each base angle is……… | (q) greater |
(c) The sum of three medians of a triangle is ………… than the perimeter. | (r) 30° |
(d) In a triangle, the sum of any two sides is always …….. than the third side. | (s) 55° |
The correct answer is:
(a)-……, (b)-……, (c)-……., (d)-……
a) In ∆ABC, ∠ A=70°
As AB = AC and we know that angles opposite to equal sides are equal
∴ In triangle ABC,
∠ A + ∠ B + ∠ C = 180o
70o + 2∠ C = 180o
2∠ C = 180o – 70o
∠ C = 
∴ ∠ C = 55o
(b) We know that,
Angles opposite to equal sides are equal
It is given that, vertical angle of the isosceles triangle = 120o
Let the base angle be x
∴ 120° + x + x = 180°
120° + 2x = 180°
2x = 180° – 120°
2x = 60°
x = 
x = 30°
Hence, each base angle of the isosceles triangle is equal to 30o
(c) We know that,
The sum of the three medians of the triangle is always less than the perimeter
(d) We know that,
In a triangle the sum of any two sides is always greater than the third side
Hence, the correct match is as follows:
(a) – (s)
(b) – (r)
(c) – (p)
(d) – (q)