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Worksheet: Types of Triangles

Q1:

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

What type of triangle is 𝐴 𝐡 𝐢 ?

  • Aisosceles
  • Bscalene
  • Cequilateral

Q2:

If 𝐴 𝐡 = 1 3 c m , 𝐡 𝐢 = 6 c m , and 𝐢 𝐴 = 9 c m , what is the type of β–³ 𝐴 𝐡 𝐢 in terms of its side lengths?

  • Aequilateral triangle
  • Bisosceles triangle
  • Cscalene triangle

Q3:

If 𝐴 𝐡 = 5 c m , 𝐡 𝐢 = 8 c m , and 𝐢 𝐴 = 1 1 c m , what is the type of β–³ 𝐴 𝐡 𝐢 in terms of its side lengths?

  • Aequilateral triangle
  • Bisosceles triangle
  • Cscalene triangle

Q4:

In the following figure,  𝐡 𝐷 bisects ∠ 𝐡 . Determine the type of β–³ 𝐸 𝐡 𝐷 in terms of its side lengths.

  • Aequilateral triangle
  • Bscalene triangle
  • Cisosceles triangle

Q5:

In the following figure,  𝐡 𝐷 bisects ∠ 𝐡 . Determine the type of β–³ 𝐸 𝐡 𝐷 in terms of its side lengths.

  • Aequilateral triangle
  • Bscalene triangle
  • Cisosceles triangle

Q6:

In the following figure,  𝐡 𝐷 bisects ∠ 𝐡 . Determine the type of β–³ 𝐸 𝐡 𝐷 in terms of its side lengths.

  • Aequilateral triangle
  • Bscalene triangle
  • Cisosceles triangle

Q7:

What type of triangle is β–³ 𝐴 𝐡 𝐢 , in terms of its side lengths?

  • Aequilateral triangle
  • Bisosceles triangle
  • Cscalene triangle

Q8:

What type of triangle is β–³ 𝐴 𝐡 𝐢 , 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 𝐴 ( βˆ’ 2 , βˆ’ 7 ) , 𝐡 ( 1 , 6 ) , and 𝐢 ( 9 , 6 ) form with respect to its sides?

  • Aisosceles triangle
  • Bequilateral triangle
  • Cscalene triangle

Q11:

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
  • 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 𝐴 𝐡 𝐢 , we have π‘š ∠ 𝐴 = 8 0 ∘ and π‘š ∠ 𝐡 π‘š ∠ 𝐢 = 4 1 : : . 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 𝐴 𝐡 is a chord in a circle with centre 𝑀 , then the triangle 𝐴 𝑀 𝐡 is .

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

Q19:

If 𝐴 𝐡 𝐢 is a triangle whose side lengths are 11 cm, 26.4 cm, and 28.6 cm and is similar to a triangle 𝑋 π‘Œ 𝑍 , determine the type of β–³ 𝑋 π‘Œ 𝑍 in terms of its angles.

  • Aacute
  • Bobtuse
  • Cright

Q20:

Suppose that in β–³ 𝐴 𝐡 𝐢 , we have 𝐴 𝐡 = 8 . 5 , 𝐡 𝐢 = 8 . 5 , and 𝐴 𝐢 = 1 1 . 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 β–³ 𝐴 𝐡 𝐢 , we have 𝐴 𝐡 = 6 , 𝐡 𝐢 = 1 3 . 5 , and 𝐴 𝐢 = 1 3 . 5 . What kind of triangle is this, in terms of its side lengths?

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

Q22:

In β–³ 𝐴 𝐡 𝐢 , suppose that ( 𝐴 𝐡 ) + ( 𝐡 𝐢 ) = 7 2 . 2 5 2 2 and 𝐴 𝐢 = 8 . 5 what kind of angle is ∠ 𝐡 ?

  • Aacute
  • Bobtuse
  • Cright

Q23:

Is β–³ 𝐴 𝐡 𝐢 a scalene, isosceles, or equilateral triangle?

  • Aequilateral triangle
  • Bisosceles triangle
  • Cscalene triangle

Q24:

Is β–³ 𝐴 𝐡 𝐢 a scalene, isosceles, or equilateral triangle?

  • Aequilateral triangle
  • Bisosceles triangle
  • Cscalene triangle

Q25:

Is β–³ 𝐴 𝐡 𝐢 a scalene, isosceles, or equilateral triangle?

  • Aequilateral triangle
  • Bisosceles triangle
  • Cscalene triangle