# Worksheet: Conditions for Similar Triangles

In this worksheet, we will practice identifying similar triangles using AA and SSS criteria.

Q1:

In the given figure, and are parallel. Using the 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:

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

• Ano
• Byes

Q6:

Triangles and in the given figure are similar. Work out the value of . Q7:

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.

Q8:

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

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 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.

Q9:

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.

Q10:

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

What does the 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.

Q11:

The figure shows three triangles: , , and . Are triangles and similar?

• Ano
• Byes

• ATriangle can first be rotated clockwise about onto , and then can be dilated from point by a scale factor of three onto ; hence, the triangles are similar.
• BNo sequence of translations, reflections, rotations, or dilations exists that can map triangle onto triangle ; therefore, the two triangles cannot be similar.

Q12:

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.

Q13:

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.

Q14:

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.

Q15:

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.

Q16:

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

Q17:

Given the following four shapes, which two are similar? • AShape 2 and Shape 4
• BShape 1 and Shape 2
• CShape 2 and Shape 3
• DShape 1 and Shape 3

Q18:

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

Q19:

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

Q20:

Are the two triangles in the figure similar? • Ayes
• Bno

Q21:

Are these two triangles similar? • Ayes
• Bno

Q22:

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

Q23:

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.

Q24:

Which of the following triangles is similar to the one seen in the given figure? • A • B • C • D • E Q25:

The figure shows three triangles: , , and . Are triangles and similar?

• Ano
• Byes