Types of Triangles
Class 7 Maths · Chapter 7: A Tale of Three Intersecting Lines · NCERT Ganita Prakash section 7.5
Learn
By sides: an equilateral triangle has all sides equal, an isosceles triangle two sides equal, and a scalene triangle all three sides different. So 4, 4, 4 is equilateral; 5, 5, 8 isosceles; 4, 5, 6 scalene.
By angles: a right-angled triangle has one right angle; an obtuse-angled triangle has one obtuse angle. An acute-angled triangle has all three angles acute. Why not just one acute angle? Because every triangle has at least two acute angles!
A triangle has at most one right or obtuse angle: two angles of 90° or more would already reach 180°. Each angle of an equilateral triangle is 180° ÷ 3 = 60°, so it is always acute-angled. An isosceles triangle can be right-angled (90°, 45°, 45°) or obtuse-angled (120°, 30°, 30°).
equilateral: 60°, 60°, 60°
A box puzzle: a spider in one corner of a box wants the far opposite corner, walking only on the faces. Zoya unfolds the box flat: the shortest walk becomes a straight line on the unfolded net, because the direct path is the shortest, just like the triangle inequality says.
Explore: sort by angles.
- Sort each triangle by its angles.
Remember
- By sides: equilateral, isosceles, scalene. By angles: acute-, right-, obtuse-angled.
- Every triangle has at least two acute angles; at most one angle can be 90° or more.
Quick check
A triangle has angles 30°, 60° and 90°. What kind is it?
- right-angled and scalene
- acute-angled
- obtuse-angled
- equilateral
Answer
right-angled and scalene. One angle is 90°, and three different angles mean three different sides.
Think about it
How many different right triangles ABC have ∠B = 90° and AC = 5 cm?
One answer
Infinitely many. ∠A can be anything between 0° and 90° (then ∠C = 90° − ∠A), and each choice gives a different triangle.
Practice
Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.