Parallel lines, quadrilaterals and triangles · Usually met around P3
Kinds of triangle
Count the equal sides, then look for a right angle.
How to do it
Method
Count the equal sides, then look for a right angle
5, 5, 3 cm: two sides equal, isosceles
Another way
Angles first
A right-angle mark → right-angled
In full
By sides: all three equal is an equilateral triangle; at least two equal is isosceles (the equal sides are its legs, the other its base); no two equal is scalene. By angles: one right angle makes a right-angled triangle. A right angle with the two sides beside it equal makes an isosceles right-angled triangle. How they relate: an equilateral triangle has all three sides equal, so it certainly has two equal — every equilateral triangle is isosceles, but not every isosceles triangle is equilateral. An isosceles right-angled triangle is both isosceles and right-angled. When naming one, choose the most exact name.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
By the lengths of its sides, what kind of triangle is this? (Choose the most exact name.)
- A. Isosceles
- B. Right-angled
- C. Scalene
- D. Equilateral
Choose the right answer
Show the answer and working
Answer: D. Equilateral
The sides are 6, 6 and 6 cm: count how many are equal.
Example 2
An isosceles triangle has two legs of 6 cm and a base of 11 cm. How long are its three sides altogether?
Show the answer and working
Answer: 23 cm
The two legs are equal: 6 + 6 + 11 = 23.
Example 3
One side of an equilateral triangle is 2 cm. How long are its three sides altogether?
Show the answer and working
Answer: 6 cm
All three sides are equal: 2 × 3 = 6.
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