Triangles (Including Types, Properties and Constructions)
ICSE Class 6 · Mathematics · Chapter 26
What this chapter covers
- Triangle and its parts
- Classification of triangles
- Altitude and median
- Angle sum property
- Constructing triangles
Key definitions
Vertices are the corner points of a triangle.
Sides are the three line segments that make a triangle.
The hypotenuse is the side of a right-angled triangle that lies opposite the right angle.
The angle sum property is the rule that the three angles of every triangle add up to 180°.
Key points
- A triangle is a closed figure made of three line segments; it has three vertices, three sides and three angles.
- Each angle of a triangle has a side opposite it, the side that does not touch its vertex.
- A triangle has an interior inside its sides and an exterior outside them.
- By sides, a triangle is equilateral (all sides equal), isosceles (two sides equal) or scalene (no sides equal).
- By angles, a triangle is acute-angled (all angles under 90°), right-angled (one angle 90°) or obtuse-angled (one angle over 90°).
- The side opposite the right angle in a right-angled triangle is the hypotenuse.
- An altitude joins a vertex to the opposite side at a right angle; a median joins a vertex to the midpoint of the opposite side.
- The three angles of every triangle add up to 180°.
- Each angle of an equilateral triangle is 60°.
- A triangle can be constructed from three sides, from two sides and the angle between them, or from two angles and the side between them.
Questions answered
How many sides, vertices and angles does a triangle have?
It has three sides, three vertices and three angles.
In △ LMN, which side is opposite ∠ M?
LN, because it is the side that does not touch vertex M.
A triangle has sides 8 cm, 6 cm and 8 cm. Name it by its sides.
It is isosceles, because two sides are equal.
The angles of a triangle are 30°, 60° and 90°. Name it by its angles.
It is right-angled, because one angle is 90°.
What is the difference between an altitude and a median?
Both start at a vertex. An altitude meets the opposite side at a right angle. A median meets the opposite side at its midpoint.
Two angles of a triangle are 40° and 75°. Find the third angle.
40 + 75 = 115, and 180 - 115 = 65. The third angle is 65°.
Can a triangle have angles of 100° and 95°? Give a reason.
No. Those two angles alone add up to 195°, which is more than 180°.
Which tools do you need to construct a triangle with sides 4 cm, 5 cm and 6 cm?
A ruler to draw the first side, and compasses to draw arcs of the other two lengths.