NCERT Solutions Ganita Prakash (Part 1) Chapter 7 .5 Types of Triangles — In-text Questions

Book page 1707 Updated on2026-09-05

Q1.

Did you spot any other type of triangle?

Answer

Yes. Besides equilateral, isosceles, scalene and right-angled triangles, the chapter also throws up acute-angled and obtuse-angled triangles.

Where it turned up	Triangle	Type
Construct, page 150	3, 4, 5	Scalene, right-angled
Construct, page 150	4, 4, 6	Isosceles, obtuse-angled
Figure it Out, page 161	3 cm, 120°, 8 cm	Scalene, obtuse-angled
Figure it Out, page 162	75°, 5 cm, 75°	Isosceles, acute-angled

Tip: Sorting by sides gives equilateral / isosceles / scalene. Sorting by angles gives acute-angled / right-angled / obtuse-angled. Every triangle has one label from each list.

Q2.

What are the other types of triangles based on angle measures?

Answer

Three types altogether — acute-angled, right-angled and obtuse-angled.

Type	Condition on the angles	Example
Acute-angled	All three angles less than 90°	60°, 60°, 60°
Right-angled	One angle exactly 90°	90°, 60°, 30°
Obtuse-angled	One angle greater than 90°	120°, 30°, 30°

Why it happens: A triangle can hold at most one angle of 90° or more, because two such angles would already use up 180° and leave nothing for the third. So looking at the biggest angle alone is enough to name the type.

Q3.

What could an acute-angled triangle be? Can we define it as a triangle with one acute angle? Why not?

Answer

An acute-angled triangle is one in which all three angles are acute. Defining it as "a triangle with one acute angle" would be useless.

Right-angled example: 90°, 60°, 30° — has two acute angles
Obtuse-angled example: 120°, 40°, 20° — has two acute angles
So "having an acute angle" does not single out anything

Why it happens: Every triangle already has at least two acute angles, because at most one angle can be 90° or more. A definition must separate one type from the others; "one acute angle" is true of all triangles, so it separates nothing. Insisting that all three angles be acute is what makes the definition useful.

Check it yourself: Try to draw a triangle with only one acute angle. You will find it impossible.

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