Worksheet: Types of Triangles: Sides

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 𝐴𝐡=13cm, 𝐡𝐢=6cm, and 𝐢𝐴=9cm, what is the type of △𝐴𝐡𝐢 in terms of its side lengths?

  • Ascalene triangle
  • Bisosceles triangle
  • Cequilateral triangle

Q3:

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

  • Aequilateral triangle
  • Bscalene triangle
  • Cisosceles triangle

Q4:

A triangle has vertices at the points 𝐴(4,2), 𝐡(6,2), and 𝐢(5,βˆ’1).

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

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

What type of triangle is 𝐴𝐡𝐢?

  • Aisosceles
  • Bscalene
  • Cequilateral

Q5:

In triangle 𝐴𝐡𝐢, we have π‘šβˆ π΄=80∘ and π‘šβˆ π΅π‘šβˆ πΆ=41::. What kind of triangle is it?

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

Q6:

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

  • Ascalene triangle
  • Bequilateral triangle
  • Cisosceles triangle

Q7:

What is the kind of triangle that the points 𝐴(βˆ’2,βˆ’7), 𝐡(1,6), and 𝐢(9,6) form with respect to its sides?

  • AScalene triangle
  • BEquilateral triangle
  • CIsosceles triangle

Q8:

Suppose that in △𝐴𝐡𝐢, we have 𝐴𝐡=8.5, 𝐡𝐢=8.5, and 𝐴𝐢=11. What kind of triangle is this, in terms of its side lengths?

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

Q9:

In △𝐴𝐡𝐢, we have π‘šβˆ π΄=60∘ and π‘šβˆ π΅=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, 𝐡𝐷 bisects ∠𝐡. Determine the type of △𝐸𝐡𝐷 in terms of its side lengths.

  • Aequilateral triangle
  • Bscalene triangle
  • Cisosceles triangle

Q11:

Determine whether △𝐡𝐢𝐷 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 𝐴𝐡 is a chord in a circle with center 𝑀, then the triangle 𝐴𝑀𝐡 is .

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

Q15:

If 𝐴𝐡𝐢 is a triangle whose side lengths are 11 cm, 26.4 cm, and 28.6 cm and is similar to a triangle π‘‹π‘Œπ‘, determine the type of β–³π‘‹π‘Œπ‘ in terms of its angles.

  • Aobtuse
  • Bacute
  • Cright

Q16:

In △𝐴𝐡𝐢, suppose that (𝐴𝐡)+(𝐡𝐢)=72.25 and 𝐴𝐢=8.5 what kind of angle is ∠𝐡?

  • Aobtuse
  • Bacute
  • Cright

Q17:

In a triangle 𝐴𝐡𝐢, if (𝐴𝐡)=(𝐡𝐢)+(𝐴𝐢), which angle is the right angle?

  • A ∠ 𝐴
  • B ∠ 𝐡
  • C ∠ 𝐢

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 △𝐴𝐡𝐢, with 𝐴𝐡=9, 𝐡𝐢=10, and 𝐴𝐢=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 𝐴𝐡=5cm, 𝐡𝐢=8cm, and 𝐢𝐴=11cm, what is the type of △𝐴𝐡𝐢 in terms of its side lengths?

  • Aequilateral triangle
  • Bscalene triangle
  • Cisosceles triangle

Q22:

In the following figure, 𝐡𝐷 bisects ∠𝐡. Determine the type of △𝐸𝐡𝐷 in terms of its side lengths.

  • Aisosceles triangle
  • Bequilateral triangle
  • Cscalene triangle

Q23:

In the following figure, 𝐡𝐷 bisects ∠𝐡. Determine the type of △𝐸𝐡𝐷 in terms of its side lengths.

  • Ascalene triangle
  • Bequilateral triangle
  • Cisosceles triangle

Q24:

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

  • Aequilateral triangle
  • Bisosceles triangle
  • Cscalene triangle

Q25:

What is the kind of triangle that the points 𝐴(βˆ’2,βˆ’2), 𝐡(4,9), and 𝐢(7,9) form with respect to its sides?

  • AIsosceles triangle
  • BScalene triangle
  • CEquilateral triangle

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.