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Worksheet: Similarity

Q1:

Complete the sentence: These figures are .

  • Asimilar but not congruent
  • Bneither similar nor congruent
  • Ccongruent

Q2:

Two triangles are similar. What will be true of the lengths of the corresponding sides of both triangles?

  • A If the angles are equal, the sides will be equal.
  • B They will be equal.
  • C Only two corresponding sides will be equal.
  • D They will be in a constant ratio.

Q3:

Two triangles are similar. What will be true of the measures of the corresponding angles in the two triangles?

  • A Only two corresponding angles will be equal.
  • B They will be different.
  • C If the sides are equal, the angles will be equal.
  • D They will be equal.
  • EOnly two corresponding angles will be equal.

Q4:

The two triangles in the given figure have equal angles. Is this enough to prove that the two triangles are similar?

  • A yes
  • B no

Q5:

Which of the following triangles is similar to the one seen in the given figure?

  • A
  • B
  • C
  • D
  • E

Q6:

The figure shows two triangles: and .

Work out the measure of .

What does the criterion tell us about these two triangles?

  • AAs both triangles share two angles of equal measures, they must be similar.
  • BAs both triangles share one angle of equal measure, then they must be similar.
  • CAs both triangles share two sides of equal measures, they must be similar.
  • DAs both triangles share three angles of equal measures, they must be similar.
  • EAs both triangles share two angles and two sides of equal measures, they must be similar.

Q7:

In the figure, given that the two triangles are similar, work out the value of .

  • A
  • B
  • C
  • D
  • E

Q8:

In the figure, given that the two triangles are similar, what is the scale factor that would take you from the larger to the smaller triangle?

  • A
  • B2
  • C
  • D
  • E

Q9:

Triangles and in the given figure are similar. Work out the value of .

Q10:

Find the length of .

Q11:

Two quadrilaterals have corresponding angles that have equal measures. Can we be sure that the quadrilaterals are similar?

  • A no
  • B yes

Q12:

Is the polygon similar to the polygon ?

  • Ayes
  • Bno