Year 9 Interactive Maths - Second Edition

Triangles

Architects and builders use triangles as they provide greater rigidity to the structure of a building.  Most roofs have a triangular cross-section.  In this section, we will consider the main features of triangles and their use in solving numerical problems.

A triangle is a closed plane figure bounded by three line segments.

Recall that:

The angle sum of a triangle is 180º.

Types of Triangles

There are four basic types of triangles:

Scalene triangles

A scalene triangle has no equal sides.

Isosceles triangles

An isosceles triangle has two sides equal.

The angles opposite the equal sides are equal.

An equilateral triangle has all sides equal.

All angles of an equilateral triangle are 60º.

Right triangles

A right triangle has one angle of 90º, called a right angle.

The side opposite the right angle is called the hypotenuse.  The hypotenuse is the longest side of the triangle (use a ruler to verify this).

Note:

In the diagrams, equal lengths and equal angles are each marked in the same way.

Example 7

Find the values of the pronumerals x and y in the following diagram.

Solution:

So x = 40, y = 100.

Example 8

Find the values of the pronumerals x and y in the following diagram.

Solution:

So x = 7, y = 82.

Example 9

Find the value of the pronumeral x in the following diagram.

Solution:

So, x = 12.

Example 10

Find the values of the pronumerals x and y in the following diagram.

Solution:

So, x = 18, y = 9.

Example 11

Find the value of the pronumeral x in the following diagram.

Solution:

So, x = 6.

Key Terms

triangle, angle sum of a triangle, scalene triangle, isosceles triangle, equilateral triangle, right triangle, right angle, hypotenuse