# Worksheet: Similar Shapes

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