Question

Fill in the blanks with the appropriate alphabet or numeral.
I.Two line segments are congruent, if _____________
II.Two angles are congruent, if ________
III.Two circles are congruent, if ________

Answer 1

Hint: Here first of all, let's recall the definitions of the terms used in the questions one by one and then fill in the blank with the words or applicable symbol.

Complete step-by-step answer:
A.Two line segments are said to be congruent if the measure of both the line-segments are equal.
For example: If \[\overline {AB} = 5\;cm\] and \[\overline {CD} = 5\;cm\] then both the line-segments are called congruent, since the measure of both the line-segments are equal.
Two line segments are congruent, if both the line segments are of same length.
So, the correct answer is “both the line segments are of same length”.

B.Two angles are said to be congruent if both the angles are exactly with the same measure in radians or in degrees.
For example: If $\angle A = 60^\circ $ and $\angle B = 60^\circ $ , then both the angles are said to be congruent, since both the angles are equal in measure.
Two angles are congruent, if measures of both the angles are equal.
So, the correct answer is “if measures of both the angles are equal”.

(C) The congruent circles are the circles having the same size. Size here is the “radii” but it can be diameter, circumference, area and many more.
Two circles are congruent, if both the circles have equal radius.
So, the correct answer is “both the circles have equal radius”.

Note: Know the difference between the concentric and the congruent circles. Concentric circles are the circles with the same centre but different radius. The concentric circles can be drawn as many as one wants, two or more with the same centre but different radius whereas the congruent circles are the circles with the same radius but different centres.