# Lesson Worksheet: Similarity of Triangles Mathematics • 8th Grade

In this worksheet, we will practice determining and proving whether two triangles are similar using equality of corresponding angles or proportionality of corresponding sides and practice using similarity to find unknown lengths and angles.

Q1:

In the given figure, and are parallel. Using the AA criterion, what can we say about triangles and ? • AThey are congruent.
• BThey are neither similar nor congruent.
• CThey are isosceles triangles.
• DThey are similar.
• EThey are equilateral triangles.

Q2:

Given that and are parallel, are triangles and similar? If yes, why? • ANo
• BYes, as the side lengths are equal.
• CYes, as all the corresponding angles in each triangle have equal measures.

Q3:

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

Q4:

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

• AThey will be different.
• BThey will be equal.
• COnly one corresponding angles will be equal.
• DOnly two corresponding angles will be equal.
• EIf the sides are equal, the angles will be equal.

Q5:

What does the AA criterion for triangles allow us to prove?

• AIf two corresponding angles in two triangles have equal measures, then they must be similar.
• BIf the corresponding sides of two triangles are proportional, then the two triangles are similar.
• CIf, in the two triangles, one pair of corresponding sides are proportional and the included angles are equal, then the two triangles are similar.
• DIf a corresponding side and angle are equal in two triangles, then the two triangles are similar.
• EIf the corresponding sides of two triangles are equal, then the two triangles are congruent.

Q6:

The figure shows two triangles: and . Work out the measure of angle .

What does the AA criterion tell us about these two triangles?

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

Q7:

The figure shows two triangles: and . Work out the measure of angle .

What does the AA criterion tell us about these two triangles?

• AAs both triangles only share one angle of equal measures, they are not similar.
• BAs both triangles only share one side of equal measures, they are not similar.
• CAs both triangles only share two sides of equal measures, they are not similar.
• DAs both triangles only share two angles of equal measures, they are not similar.
• EAs both triangles only share three angles of equal measures, they are not similar.

Q8:

The figure shows two triangles: and . Work out the measure of angle .

What does the AA criterion tell us about these two triangles?

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

Q9:

In the given figure, is constructed on the triangle parallel to . What can we conclude about the measure of angles and ?

• A
• B
• C
• D
• E

Using the criterion, what can we conclude about triangles and ?

• AThey are neither similar nor congruent.
• BThey are similar.
• CThey are congruent.
• DThey are isosceles triangles.
• EThey are equilateral triangles.

Q10:

The figure shows two triangles. Are the two triangles similar?

• ANo
• BYes

Why?

• AIf you calculate the measure of the third angle in one of the triangles, you can see that the triangles share two angles; therefore, by the criteria, the triangles are similar.
• BThe triangles do not share the same angles and, hence, are not similar.

Q11:

The figure shows a triangle where the line segment is parallel to Which angle is equivalent to ? Give reasons.

• A, because the angles are corresponding.
• B, because the angles are corresponding.
• C, because the angles are corresponding.
• D, because the angles are alternate.
• E, because the angles are alternate.

Which angle is equivalent to ? Give reasons.

• A, because the angles are corresponding.
• B, because the angles are corresponding.
• C, because the angles are corresponding.
• D, because the angles are alternate.
• E, because the angles are alternate.

Hence, are triangles and similar? If yes, state why?

• AYes, they are similar by the SAS criterion.
• BNo
• CYes, they are similar by the AA criterion.
• DYes, they are similar by the SSS criterion.

Q12:

The figure shows two triangles and where the line segment is parallel to . Which angle is equivalent to ? Give reasons

• A, because the angles are alternate
• B, because the angles are corresponding
• C, because the angles are corresponding
• D, because the angles are vertically opposite
• E, because the angles are alternate

Which angle is equivalent to ? Give reasons

• A, because the angles are corresponding
• B, because the angles are alternate
• C, because the angles are alternate
• D, because the angles are corresponding
• E, because the angles are vertically opposite

Hence, are triangles and similar? If yes, state why.

• ANo
• BYes, they are similar by the SSS criterion.
• CYes, they are similar by the AA criterion.
• DYes, they are similar by the SAS criterion.

Q13:

Triangles and in the given figure are similar. What, if anything, must be true of the lines and ? • AThey are parallel.
• BThey are perpendicular.

Q14:

The figure shows two triangles. Find the measure of angle .

Find the measure of angle .

The triangles, therefore, share the same angles and are similar. What is the fewest number of angles needed to determine whether two triangles are similar?

• Aone
• Btwo
• Cthree

Q15:

The figure shows two triangles. Find the measure of angle .

Find the measure of angle .

Are the two triangles similar?

• ANo
• BYes

What is the fewest number of angles needed to determine whether two triangles are similar?

• Athree
• Bone
• Ctwo

Q16:

Are the two triangles in the figure similar? • AYes
• BNo

Q17:

Are these two triangles similar? • AYes
• BNo

Q18:

In the given figure, triangles and are similar. What must be true of and ? • A
• B
• C
• D
• E

Q19:

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 two angles and two sides of equal measures, 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 one angle of equal measure, then they must be similar.

Q20:

Which of the following triangles is similar to the one seen in the given figure? • A • B • C • D • E Q21:

In the two triangles shown, and . What is ? Q22:

Which two of these triangles are similar? • A,
• B,
• C,
• D,

Q23:

Two triangles contain angles with measures of and . Are the two triangles similar? If yes, why? • ANo
• BYes, because they have different angles.
• CYes, by the AA criterion

Q24:

Which of the following properties is enough to conclude that two triangles are similar?

• AAll corresponding angles have the same ratio.
• BThey have the same measure of angles.
• CTwo corresponding sides have the same ratio.
• DThey both contain a right angle.
• EOne corresponding side and one corresponding angle are equal.

Q25:

Fill in the blank: . • A,
• B,
• C,
• D,