Worksheet: Types of Triangles: Sides

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In this worksheet, we will practice classifying triangles as equilateral, isosceles, or scalene based on their sides.

Q1:

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

  • Aright triangles
  • Bscalene triangles
  • Cequilateral triangles
  • Disosceles triangles

Q2:

If 𝐴𝐵=13cm, 𝐵𝐶=6cm, and 𝐶𝐴=9cm, what is the type of △𝐴𝐵𝐶 in terms of its side lengths?

  • Ascalene triangle
  • Bisosceles triangle
  • Cequilateral triangle

Q3:

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

  • Aequilateral triangle
  • Bscalene triangle
  • Cisosceles triangle

Q4:

A triangle has vertices at the points 𝐴(4,2), 𝐵(6,2), and 𝐶(5,−1).

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

  • A 𝐴 𝐵 = 1 2 , 𝐴 𝐶 = 1 0 , and 𝐵𝐶=2
  • B 𝐴 𝐵 = 2 , 𝐴 𝐶 = √ 1 0 , and 𝐵𝐶=√10
  • C 𝐴 𝐵 = 2 √ 3 , 𝐴 𝐶 = √ 1 4 , and 𝐵𝐶=√2
  • D 𝐴 𝐵 = 4 , 𝐴 𝐶 = 3 √ 2 , and 𝐵𝐶=√2
  • E 𝐴 𝐵 = 2 √ 3 , 𝐴 𝐶 = 2 √ 1 1 , and 𝐵𝐶=√10

What type of triangle is 𝐴𝐵𝐶?

  • Aisosceles
  • Bscalene
  • Cequilateral

Q5:

In triangle 𝐴𝐵𝐶, we have 𝑚∠𝐴=80∘ and 𝑚∠𝐵𝑚∠𝐶=41::. What kind of triangle is it?

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

Q6:

Is △𝐴𝐵𝐶 a scalene, isosceles, or equilateral triangle?

  • Ascalene triangle
  • Bequilateral triangle
  • Cisosceles triangle

Q7:

What is the kind of triangle that the points 𝐴(−2,−7), 𝐵(1,6), and 𝐶(9,6) form with respect to its sides?

  • AScalene triangle
  • BEquilateral triangle
  • CIsosceles triangle

Q8:

Suppose that in △𝐴𝐵𝐶, we have 𝐴𝐵=8.5, 𝐵𝐶=8.5, and 𝐴𝐶=11. What kind of triangle is this, in terms of its side lengths?

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

Q9:

In △𝐴𝐵𝐶, we have 𝑚∠𝐴=60∘ and 𝑚∠𝐵=60∘. What type of triangle is this, in terms of the lengths of its sides?

  • Ascalene triangle
  • Bequilateral triangle
  • Cisosceles triangle

Q10:

In the following figure, 𝐵𝐷 bisects ∠𝐵. Determine the type of △𝐸𝐵𝐷 in terms of its side lengths.

  • Aequilateral triangle
  • Bscalene triangle
  • Cisosceles triangle

Q11:

Determine whether △𝐵𝐶𝐷 is an obtuse or acute triangle.

  • Aacute
  • Bobtuse

Q12:

Is this a scalene, isosceles, or right triangle?

  • ARight triangle
  • BIsosceles triangle
  • CScalene triangle

Q13:

What do these shapes have in common?

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

Q14:

Complete the following: If 𝐴𝐵 is a chord in a circle with center 𝑀, then the triangle 𝐴𝑀𝐵 is .

  • Aan equilateral triangle
  • Ban isosceles triangle
  • Ca scalene triangle

Q15:

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

  • Aobtuse
  • Bacute
  • Cright

Q16:

In △𝐴𝐵𝐶, suppose that (𝐴𝐵)+(𝐵𝐶)=72.25 and 𝐴𝐶=8.5 what kind of angle is ∠𝐵?

  • Aobtuse
  • Bacute
  • Cright

Q17:

In a triangle 𝐴𝐵𝐶, if (𝐴𝐵)=(𝐵𝐶)+(𝐴𝐶), which angle is the right angle?

  • A ∠ 𝐴
  • B ∠ 𝐵
  • C ∠ 𝐶

Q18:

What do these shapes have in common?

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

Q19:

Two angles in a triangle are 83∘ and 48∘. What kind of triangle is it, in terms of its angles?

  • Aacute-angled
  • Bright-angled
  • Cobtuse -angled

Q20:

Consider △𝐴𝐵𝐶, with 𝐴𝐵=9, 𝐵𝐶=10, and 𝐴𝐶=11. What kind of triangle is this, in terms of its angles?

  • Aan acute-angled triangle
  • Ba right-angled triangle
  • Can obtuse-angled triangle

Q21:

If 𝐴𝐵=5cm, 𝐵𝐶=8cm, and 𝐶𝐴=11cm, what is the type of △𝐴𝐵𝐶 in terms of its side lengths?

  • Aequilateral triangle
  • Bscalene triangle
  • Cisosceles triangle

Q22:

In the following figure, 𝐵𝐷 bisects ∠𝐵. Determine the type of △𝐸𝐵𝐷 in terms of its side lengths.

  • Aisosceles triangle
  • Bequilateral triangle
  • Cscalene triangle

Q23:

In the following figure, 𝐵𝐷 bisects ∠𝐵. Determine the type of △𝐸𝐵𝐷 in terms of its side lengths.

  • Ascalene triangle
  • Bequilateral triangle
  • Cisosceles triangle

Q24:

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

  • Aequilateral triangle
  • Bisosceles triangle
  • Cscalene triangle

Q25:

What is the kind of triangle that the points 𝐴(−2,−2), 𝐵(4,9), and 𝐶(7,9) form with respect to its sides?

  • AIsosceles triangle
  • BScalene triangle
  • CEquilateral triangle

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