Triangle Similarity Problem: Comparing Angles of 70° and 35°

Q: Do I need to check all three angles for similarity?

No! The Angle-Angle (AA) theorem says you only need two pairs of equal angles. The third pair will automatically be equal since all triangles have angles that sum to 180°.

Q: How do I know which angles correspond to each other?

Look at the position and labeling of vertices. In this problem, angle B corresponds to angle E (both 70°), and angle C corresponds to angle F (both 35°).

Q: What if the triangles look different sizes?

Similar triangles can be different sizes! Similarity means they have the same shape but not necessarily the same size. Equal angles guarantee the same shape.

Q: Can triangles be similar if no angles are given?

Yes! You can also prove similarity using Side-Side-Side (SSS) or Side-Angle-Side (SAS) similarity theorems, but you need to know side lengths or ratios.

Q: What's the difference between similar and congruent triangles?

Similar triangles have the same shape (equal angles) but can be different sizes. Congruent triangles have the same shape AND the same size (all angles and sides equal).

Triangle Similarity with Angle-Angle Comparison

Angle B is equal to 70 degrees

Angle C is equal to 35 degrees

Angle E is equal to 70 degrees

Angle F is equal to 35 degrees

Are the triangles similar?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Are the triangles similar?

00:03 The sum of angles in a triangle equals 180

00:10 Let's substitute appropriate values and solve for angle A

00:17 This is the size of angle A

00:22 Let's use the same method in the second triangle

00:29 Let's substitute appropriate values and solve for angle D

00:36 This is the size of angle D

00:39 All angles are equal between the triangles, therefore they are similar by AA similarity

00:44 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Angle B is equal to 70 degrees

Angle C is equal to 35 degrees

Angle E is equal to 70 degrees

Angle F is equal to 35 degrees

Are the triangles similar?

Step-by-step solution

The triangles are similar according to the angle-angle theorem.

Having two pairs of equal angles is sufficient to conclude that the triangles are similar.

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic

Angle-Angle (AA) Rule: Two pairs of equal angles prove triangle similarity
Technique: Compare corresponding angles: 70° = 70° and 35° = 35°
Check: Third angles must also equal: 180° - 70° - 35° = 75° ✓

Common Mistakes

Avoid these frequent errors

Only comparing one pair of angles
Don't just check if one angle equals another = incomplete proof! You need at least two pairs of equal angles to prove similarity. Always compare at least two corresponding angle pairs before concluding triangles are similar.

Practice Quiz

Test your knowledge with interactive questions

Angle B is equal to 60°

Angle C is equal to 55°

Angle E is equal to 60°

Angle F is equal to 50°

Are these triangles similar?

FAQ

Everything you need to know about this question

Do I need to check all three angles for similarity?

No! The Angle-Angle (AA) theorem says you only need two pairs of equal angles. The third pair will automatically be equal since all triangles have angles that sum to 180°.

How do I know which angles correspond to each other?

Look at the position and labeling of vertices. In this problem, angle B corresponds to angle E (both 70°), and angle C corresponds to angle F (both 35°).

What if the triangles look different sizes?

Similar triangles can be different sizes! Similarity means they have the same shape but not necessarily the same size. Equal angles guarantee the same shape.

Can triangles be similar if no angles are given?

Yes! You can also prove similarity using Side-Side-Side (SSS) or Side-Angle-Side (SAS) similarity theorems, but you need to know side lengths or ratios.

What's the difference between similar and congruent triangles?

Similar triangles have the same shape (equal angles) but can be different sizes. Congruent triangles have the same shape AND the same size (all angles and sides equal).

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