NCERT Solutions for Class 5th Maths Chapter 7 Angles of an equilateral triangle, and the scalene triangle — Try This
Book page 97 Updated on2026-09-19
Q1.
Cut the equilateral triangle provided at the end of the book. Check if all the angles of an equilateral triangle are equal — just like you did with the isosceles triangle.
Answer
Yes. All three angles of an equilateral triangle are equal.
How to check by folding
Cut out the equilateral triangle. Its three sides are all the same length — measure them to be sure.
Fold once. Bring corner A onto corner B. Corner A sits exactly on corner B, so angle A = angle B.
Open it out and fold again, this time bringing corner B onto corner C. They match too, so angle B = angle C.
Put the two results together. If A = B and B = C, then all three are equal.
Each fold line goes from a corner to the middle of the opposite side.
Angle A = Angle B (first fold) Angle B = Angle C (second fold) So Angle A = Angle B = Angle C Each angle = 180 ÷ 3 = 60
Why it must be so: Equal sides give equal angles. An equilateral triangle has three equal sides, so it has three equal angles. And since the three angles of any triangle add up to 180, each one here is 60.
Now you know why six of them fit round a point: 60 × 6 = 360. That is the same fact you found in the Find Out box.
Q2.
Now, cut the equilateral triangle in half. How many sides of each new triangle are equal?
Answer
None. All three sides of each new triangle are different lengths. A triangle like that is called a scalene triangle.
What happens when you cut
Fold the equilateral triangle in half and cut along the fold. You get two smaller triangles, and they are alike.
Look at one of them. Its longest side is a whole side of the big triangle.
Its shortest side is half of another side of the big triangle — so it is only half as long.
Its third side is the cut line, which is neither of those two lengths.
Measure all three. You get three different numbers. No two sides are equal.
The half-triangle also has a square corner where the cut meets the base.
Why the sides are all different: The cut goes from a corner down to the middle of the opposite side. So one new side is a full side of the big triangle, another is only half of a side, and the cut itself is shorter than a full side but longer than half of one. Three different lengths.
New word:Scalene means “uneven”. A scalene triangle has no equal sides.
Q3.
Check in scalene triangles whether any two or more angles are equal?
Answer
No two angles of a scalene triangle are equal. All three angles are different.
How to check by folding
Take one of your half-triangles.
Try to fold one corner onto another. Try every pair: first with second, second with third, first with third.
Watch what happens. In every try the two corners do not cover each other — one always pokes out past the other.
So no two angles are equal.
In the half of an equilateral triangle: the square corner = 90 the corner kept from the big triangle = 60 the third corner = 180 − 90 − 60 = 30 90, 60 and 30 are all different ✓
The rule behind it: Equal sides go with equal angles, and unequal sides go with unequal angles. A scalene triangle has no two sides equal, so it can have no two angles equal either.
The three families together: equilateral — 3 equal sides, 3 equal angles. Isosceles — 2 equal sides, 2 equal angles. Scalene — no equal sides, no equal angles. The sides and the angles always tell the same story.