# Lesson Worksheet: Angle-Angle Triangle Similarity Mathematics • 11th Grade

In this worksheet, we will practice determining whether two triangles are similar using the equality of corresponding angles (Angle-Angle criteria) and using the similarity to find unknown angles.

Q1:

Find the length of . Q2:

The figure shows triangle . Work out the value of .

Work out the value of .

Work out the perimeter of .

Q3:

In the given figure, lies on both and . and each have a length of 4, and has a length of 3. Calculate the length of .

• A
• B5
• C4
• D3
• E

Calculate the length of .

Hence, calculate the length of .

• A
• B1
• C
• D3
• E4

Q4:

Determine the length of . Q5:

If , find the length of . Q6:

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

Find the length of . Q9:

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

Q10:

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.