Worksheet: Types of Triangles Based on 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?

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

Q2:

If 𝐴 𝐵 = 1 3 c m , 𝐵 𝐶 = 6 c m , and 𝐶 𝐴 = 9 c m , what is the type of △ 𝐴 𝐵 𝐶 in terms of its side lengths?

  • Aequilateral triangle
  • Bisosceles triangle
  • Cscalene triangle

Q3:

What type of triangle is △ 𝐴 𝐵 𝐶 , in terms of its side lengths?

  • Aequilateral triangle
  • Bisosceles triangle
  • Cscalene 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 = 2 √ 3 , 𝐴 𝐶 = 2 √ 1 1 , and 𝐵 𝐶 = √ 1 0
  • B 𝐴 𝐵 = 4 , 𝐴 𝐶 = 3 √ 2 , and 𝐵 𝐶 = √ 2
  • C 𝐴 𝐵 = 2 √ 3 , 𝐴 𝐶 = √ 1 4 , and 𝐵 𝐶 = √ 2
  • D 𝐴 𝐵 = 2 , 𝐴 𝐶 = √ 1 0 , and 𝐵 𝐶 = √ 1 0
  • E 𝐴 𝐵 = 1 2 , 𝐴 𝐶 = 1 0 , and 𝐵 𝐶 = 2

What type of triangle is 𝐴 𝐵 𝐶 ?

  • Aisosceles
  • Bscalene
  • Cequilateral

Q5:

In triangle 𝐴 𝐵 𝐶 , we have 𝑚 ∠ 𝐴 = 8 0 ∘ and 𝑚 ∠ 𝐵 𝑚 ∠ 𝐶 = 4 1 : : . What kind of triangle is it?

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

Q6:

Is △ 𝐴 𝐵 𝐶 a scalene, isosceles, or equilateral triangle?

  • Aequilateral triangle
  • Bisosceles triangle
  • Cscalene 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?

  • Aisosceles triangle
  • Bequilateral triangle
  • Cscalene triangle

Q8:

Suppose that in △ 𝐴 𝐵 𝐶 , we have 𝐴 𝐵 = 8 . 5 , 𝐵 𝐶 = 8 . 5 , and 𝐴 𝐶 = 1 1 . What kind of triangle is this, in terms of its side lengths?

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

Q9:

In △ 𝐴 𝐵 𝐶 , we have 𝑚 ∠ 𝐴 = 6 0 ∘ and 𝑚 ∠ 𝐵 = 6 0 ∘ . What type of triangle is this, in terms of the lengths of its sides?

  • Ascalene triangle
  • Bisosceles triangle
  • Cequilateral triangle

Q10:

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

  • Aequilateral triangle
  • Bscalene triangle
  • Cisosceles triangle

Q11:

Determine whether △ 𝐵 𝐶 𝐷 is an obtuse or acute triangle.

  • Aacute
  • Bobtuse

Q12:

Is this a scalene, isosceles, or right triangle?

  • AIsosceles triangle
  • BRight triangle
  • CScalene triangle

Q13:

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.

Q14:

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

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

Q15:

If 𝐴 𝐵 𝐶 is a triangle whose side lengths are 11 cm, 26.4 cm, and 28.6 cm and is similar to a triangle 𝑋 𝑌 𝑍 , determine the type of △ 𝑋 𝑌 𝑍 in terms of its angles.

  • Aacute
  • Bobtuse
  • Cright

Q16:

In △ 𝐴 𝐵 𝐶 , suppose that ( 𝐴 𝐵 ) + ( 𝐵 𝐶 ) = 7 2 . 2 5 2 2 and 𝐴 𝐶 = 8 . 5 what kind of angle is ∠ 𝐵 ?

  • Aacute
  • Bobtuse
  • Cright

Q17:

In a triangle 𝐴 𝐵 𝐶 , if ( 𝐴 𝐵 ) = ( 𝐵 𝐶 ) + ( 𝐴 𝐶 ) 2 2 2 , which angle is the right angle?

  • A ∠ 𝐵
  • B ∠ 𝐴
  • C ∠ 𝐶

Q18:

What do these shapes have in common?

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

Q19:

Two angles in a triangle are 8 3 ∘ and 4 8 ∘ . What kind of triangle is it, in terms of its angles?

  • Aobtuse-angled
  • Bright-angled
  • Cacute-angled

Q20:

Consider △ 𝐴 𝐵 𝐶 , with 𝐴 𝐵 = 9 , 𝐵 𝐶 = 1 0 , and 𝐴 𝐶 = 1 1 . What kind of triangle is this, in terms of its angles?

  • Aa right-angled triangle
  • Ban obtuse-angled triangle
  • Can acute-angled triangle

Q21:

If 𝐴 𝐵 = 5 c m , 𝐵 𝐶 = 8 c m , and 𝐶 𝐴 = 1 1 c m , what is the type of △ 𝐴 𝐵 𝐶 in terms of its side lengths?

  • Aequilateral triangle
  • Bisosceles triangle
  • Cscalene triangle

Q22:

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

  • Aequilateral triangle
  • Bscalene triangle
  • Cisosceles triangle

Q23:

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

  • Aequilateral triangle
  • Bscalene triangle
  • Cisosceles triangle

Q24:

What type of triangle is △ 𝐴 𝐵 𝐶 , 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
  • Bequilateral triangle
  • Cscalene triangle

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