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This middle school Math quiz on shapes is going to be about triangles and their properties: triangles are very, very important in geometry. They say two is company but three is a crowd; unfortunately, you need three sides to make a triangle.

How many 3-sided shapes can you think of? There is only one - the triangle. However, there are many different types of triangles - how many can you remember? This quiz will test you on some of them - as always, don't move on until you've got all ten questions correct.

1.

Which one of the following statements is correct?

It is only possible to construct one equilateral triangle with a 90° interior angle

It is only possible to construct two equilateral triangles with a 90° interior angle

It is impossible to construct an equilateral triangle with a 90° interior angle

It is only possible to construct one equilateral triangle with two 90° interior angles

If the triangle is equilateral, then all the sides are of the same length. This means that all the interior angles will be the same: this can only happen if all the angles are equal to 60°

2.

Which one of the following statements is incorrect?

In a triangle whose sides are not the same length, the length of the longest side is shorter than the sum of the lengths of the other two sides

The longest side of a triangle is always opposite the biggest interior angle

The shortest side of a triangle is always opposite the smallest interior angle

The longest side of a triangle is sometimes opposite the smallest interior angle

Try constructing this: you will find that it is impossible to draw the triangle. The longest side of a triangle is always opposite the biggest interior angle

3.

Which one of the following statements is incorrect?

A triangle has three sides

A triangle has three vertices

The sum of the interior angles of a triangle is greater than 180°

A triangle has three interior angles

I hope that you didn't get this wrong! The sum of the interior angles of a triangle = 180°

4.

Which one of the following statements is correct?

In a right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides

In a triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides

In a triangle, the square of the length of the longest side equals the sum of the squares of the lengths of the other two sides

In a right triangle, the square of the length of one side equals the sum of the squares of the lengths of the other two sides

This is Pythagoras' Theorem

5.

Which one of the following statements is correct?

Only two equiangular triangles can be constructed

Only three equiangular triangles can be constructed

Many equiangular triangles can be constructed

Only one equiangular triangle can be constructed

An equiangular triangle is a triangle whose interior angles are all the same. The sum of the interior angles of a triangle = 180°, so each interior angle must be 60°, BUT many such triangles exist: although the interior angles may all be the same, you can have different triangles. The side lengths will all be the same for each particular triangle, but a triangle with side lengths of 12 cm is not the same as, say, a triangle with side lengths of 6 cm - even though the interior angles are all 60°

6.

Which one of the following statements is correct?

In an acute triangle, only one of the interior angles is less than ninety-degrees

In an acute triangle, all of the interior angles are less than ninety-degrees

In an acute triangle, only two of the interior angles is less than ninety-degrees

In an acute triangle, the shortest side is opposite the largest acute angle

All of the angles are less than ninety-degrees

7.

Which one of the following statements is correct?

The hypotenuse of a right triangle is always opposite the smallest angle

The hypotenuse of a right triangle is always the shortest side

The hypotenuse of a right triangle is always opposite the right-angle

The longest side of a triangle is called the hypotenuse

Remember this fact - it will help you when you have to use Pythagoras' theorem

8.

Which one of the following statements is incorrect?

An obtuse triangle has two interior obtuse angles

An obtuse triangle has one interior obtuse angle

In an obtuse triangle, the longest side is opposite the obtuse angle

An obtuse triangle is a triangle that has an interior angle greater than 90°

If it had two interior obtuse angles, it would not be possible to construct such a triangle because an obtuse angle is greater than 90° and less than 180°

9.

Which one of the following statements is incorrect?

An isosceles triangle has an axis of symmetry

An isosceles triangle has two of its angles the same

An isosceles triangle has two of its sides the same length

An isosceles triangle has all of its sides equal in length

Only two of its sides are the same, so two of its angles are also the same

10.

Which one of the following statements is incorrect?

A scalene triangle has all of its interior angles different

A scalene triangle has all of its sides equal in length

A scalene triangle has all of its sides different in length

If all three angles of a triangle are different, then it's a scalene triangle

All of its sides are different, so all of its angles are also different