Grade 8 · Math

8th grade Are these triangles similar? (angle-angle) worksheet

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Are these triangles similar? (angle-angle)

Grade 8 Math Worksheet - Challenge Me

NameDate

Circle the best answer, or write your answer on the line.

1.
Esme compares two isosceles tent fronts, A and B. A's top angle is 40°. B's two base angles are 70° each. Are the triangles similar?
- No: A has a 40° angle but B has a 70° angle, so they are not similar
- Not enough to tell: we need the side lengths first
- Yes: both have the angles 40°, 70° and 70°, so they are similar
2.
Jun compares two isosceles roofs, A and B. A's top angle is 50°. B's two base angles are 55° each. Are the triangles similar?
- Yes: both are isosceles triangles, so they are similar
- Not enough to tell: we need the side lengths first
- No: A's angles are 50°, 65° and 65° but B's are 55°, 55° and 70°, so they are not similar
3.
Kira compares two isosceles sails, A and B. A's two base angles are 35° each. B's top angle is 110°. Are the triangles similar?
- No: A has a 35° angle but B has a 110° angle, so they are not similar
- Yes: both have the angles 35°, 35° and 110°, so they are similar
- Not enough to tell: we need the side lengths first
4.
Luz compares two isosceles kite wings, A and B. A's top angle is 80°. B's two base angles are 60° each. Are the triangles similar?
- Yes: both are isosceles triangles, so they are similar
- Not enough to tell: we need the side lengths first
- No: A's angles are 50°, 50° and 80° but B's are 60°, 60° and 60°, so they are not similar
5.
Bo labels the corners of two similar kite wings. Which statement is true?
- triangle DFG is similar to triangle HQS
- triangle DFG is similar to triangle QSH
- triangle DFG is similar to triangle SHQ
6.
“sketches, not to scale” Esme sorts three pairs of paper triangles by two angles each. Exactly one pair is similar. Which pair is it?
- Pair 3
- Pair 2
- Pair 1
7.
“(sketches, not to scale)” Jun sorts three pairs of paper triangles by two angles each. Exactly one pair is similar. Which pair is it?
- Pair 1
- Pair 3
- Pair 2
Milo draws two right-triangle ramps, A and B. B has a 37° angle. How many cm long is B's side across the right angle?
Pia draws two right-triangle sails, A and B. B has a 23° angle. How many cm long is B's side across the right angle?
10.
Zee says two triangles are similar when two angles match. Triangles A and B both have a 33° angle and a 52° angle. Why must their third angles match too?
- Each third angle is 33° + 52° = 85°
- Each third angle is 180° − 33° − 52° = 95°
- Each third angle is 360° − 33° − 52° = 275°
- Each third angle is the same as the first angle, 33°

8th grade Are these triangles similar? (angle-angle) worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Are these triangles similar? (two equal angles). Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can tell whether two triangles are similar from their angles alone: two equal angles are enough, because the third angles must match too.
I can find a triangle's third angle, including in an isosceles or a right triangle, and match corners and sides by their equal angles.
I can use the equal angles to pair the sides across them and find a missing side.

Standard: 8.G.A.5 (angle-angle criterion), 8.G.A.4 (partial)

Words to know

similar triangles: Same shape, maybe different size: the angles match and the sides grow by one number.

third angle: The angle left over: 180° minus the other two.

matching corners: Corners with equal angles, in the same place on each triangle.

across from an angle: The side that sits opposite that corner, not touching it.

isosceles triangle: A triangle with two equal sides. Its two base angles are equal.

right triangle: A triangle with one 90° angle. Its other two angles add to 90°.

similarity statement: A sentence like "triangle CDF is similar to triangle WVU". Its letters pair up in order.

Common mistakes

Matched angles, corners or sides by where they sit in a list or in the alphabet, not by their size.

Thought one equal angle is enough to call two triangles similar. Draw two different triangles that both have a 50° angle and compare them.

Thought we need the side lengths to tell whether two triangles are similar.

What to say

Ask: which angle in the second triangle is equal to this one?

Ask: if two angles of one triangle equal two angles of the other, what must the third angles be?

Questions parents ask

What is the most common mistake with are these triangles similar? (angle-angle)?

Matched angles, corners or sides by where they sit in a list or in the alphabet, not by their size.

How can I help my child with are these triangles similar? (angle-angle)?

Ask: which angle in the second triangle is equal to this one?

Are these 8th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More grade 8 math

See all grade 8 math

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