# Worksheet: Types of Triangles

Q1:

A triangle has vertices at the points , , and .

Work out the lengths of the sides of the triangle. Give your answers as surds in their simplest form.

• A , , and
• B , , and
• C , , and
• D , , and
• E , , and

What type of triangle is ?

• Aisosceles
• Bscalene
• Cequilateral

Q2:

If , , and , what is the type of in terms of its side lengths?

• Aequilateral triangle
• Bisosceles triangle
• Cscalene triangle

Q3:

If , , and , what is the type of in terms of its side lengths?

• Aequilateral triangle
• Bisosceles triangle
• Cscalene triangle

Q4:

In the following figure, bisects . Determine the type of in terms of its side lengths.

• Aequilateral triangle
• Bscalene triangle
• Cisosceles triangle

Q5:

In the following figure, bisects . Determine the type of in terms of its side lengths.

• Aequilateral triangle
• Bscalene triangle
• Cisosceles triangle

Q6:

In the following figure, bisects . Determine the type of in terms of its side lengths.

• Aequilateral triangle
• Bscalene triangle
• Cisosceles triangle

Q7:

What type of triangle is , in terms of its side lengths?

• Aequilateral triangle
• Bisosceles triangle
• Cscalene triangle

Q8:

What type of triangle is , in terms of its side lengths?

• Aequilateral triangle
• Bisosceles triangle
• Cscalene triangle

Q9:

Determine whether is an obtuse-angled or acute-angled triangle.

• Aacute-angled
• Bobtuse-angled

Q10:

What is the kind of triangle that the points , , and form with respect to its sides?

• Aisosceles triangle
• Bequilateral triangle
• Cscalene triangle

Q11:

What is the kind of triangle that the points , , and form with respect to its sides?

• Aisosceles triangle
• Bequilateral triangle
• Cscalene triangle

Q12:

In , we have and . What type of triangle is this, in terms of the lengths of its sides?

• Ascalene triangle
• Bisosceles triangle
• Cequilateral triangle

Q13:

In , we have and . What type of triangle is this, in terms of the lengths of its sides?

• Aequilateral triangle
• Bisosceles triangle
• Cscalene triangle

Q14:

Is this a scalene, isosceles, or right triangle?

• AIsosceles triangle
• BRight triangle
• CScalene triangle

Q15:

What kind of triangles have all sides of the same length?

• Aisosceles triangles
• Bright triangles
• Cscalene triangles
• Dequilateral triangles

Q16:

In triangle , we have and . What kind of triangle is it?

• Aa scalene triangle
• Ban equilateral triangle
• Can isosceles triangle

Q17:

What do these shapes have in common?

• ABoth are right triangles.
• BBoth are isosceles triangles.
• CBoth are acute triangles.
• DBoth are obtuse triangles.
• EBoth are equilateral triangles.

Q18:

Complete the following: If is a chord in a circle with centre , then the triangle is .

• A a scalene triangle
• B an equilateral triangle
• C an isosceles triangle

Q19:

If is a triangle whose side lengths are 11 cm, 26.4 cm, and 28.6 cm and is similar to a triangle , determine the type of in terms of its angles.

• Aacute
• Bobtuse
• Cright

Q20:

Suppose that in , we have , , and . What kind of triangle is this, in terms of its side lengths?

• Aan equilateral triangle
• Ba scalene triangle
• Can isosceles triangle

Q21:

Suppose that in , we have , , and . What kind of triangle is this, in terms of its side lengths?

• Aan equilateral triangle
• Ba scalene triangle
• Can isosceles triangle

Q22:

In , suppose that and what kind of angle is ?

• Aacute
• Bobtuse
• Cright

Q23:

Is a scalene, isosceles, or equilateral triangle?

• Aequilateral triangle
• Bisosceles triangle
• Cscalene triangle

Q24:

Is a scalene, isosceles, or equilateral triangle?

• Aequilateral triangle
• Bisosceles triangle
• Cscalene triangle

Q25:

Is a scalene, isosceles, or equilateral triangle?

• Aequilateral triangle
• Bisosceles triangle
• Cscalene triangle