Similar Triangles with 25° Angles: Identifying the Correct Theorem

Q: Why isn't one equal angle enough to prove similarity?

While the triangles both have 25° angles, you need at least two pieces of information to prove similarity. Think of it like this: many different triangles can have a 25° angle but still have completely different shapes!

Q: What information would I need to prove these triangles are similar?

You'd need one of these: AA: A second pair of equal anglesSSS: All three pairs of sides are proportionalSAS: Two pairs of proportional sides with the included angle equal

Q: Could the triangles still be similar even though we can't prove it?

Possibly! The triangles might be similar, but we can't prove it with the given information. In math, we can only conclude what we can definitively prove from the given data.

Q: How do I check if sides are proportional?

Compare ratios of corresponding sides. For example, if $ \frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF} $, then the sides are proportional and you can use SSS similarity.

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

Congruent triangles are exactly the same size and shape. Similar triangles have the same shape but can be different sizes - their corresponding angles are equal and sides are proportional.

Triangle Similarity with Insufficient Information

Are the two triangles similar?

If so, according to which theorem?

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Step-by-step video solution

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00:00 Are the triangles similar?

00:06 Angles are equal according to given data

00:13 Let's try to find the similarity ratio

00:27 Let's substitute appropriate values according to the given data

00:44 We don't have enough data to determine if they are similar

00:50 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

Are the two triangles similar?

If so, according to which theorem?

Step-by-step solution

Since we neither have data on sides AB and DE nor the other angles, it is impossible to know.

Final Answer

It is impossible to know.

Key Points to Remember

Essential concepts to master this topic

Rule: Need at least two angles or proportional sides to prove similarity
Technique: One shared angle (25°) isn't enough; need second condition
Check: Verify all similarity theorem requirements are met before concluding ✓

Common Mistakes

Avoid these frequent errors

Assuming one equal angle proves similarity
Don't think triangles are similar just because they share one 25° angle = wrong conclusion! One angle alone doesn't guarantee similarity. Always check you have AA (two angles), SSS (proportional sides), or SAS (proportional sides with included angle).

Practice Quiz

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FAQ

Everything you need to know about this question

Why isn't one equal angle enough to prove similarity?

While the triangles both have 25° angles, you need at least two pieces of information to prove similarity. Think of it like this: many different triangles can have a 25° angle but still have completely different shapes!

What information would I need to prove these triangles are similar?

You'd need one of these:

AA: A second pair of equal angles
SSS: All three pairs of sides are proportional
SAS: Two pairs of proportional sides with the included angle equal

Could the triangles still be similar even though we can't prove it?

Possibly! The triangles might be similar, but we can't prove it with the given information. In math, we can only conclude what we can definitively prove from the given data.

How do I check if sides are proportional?

Compare ratios of corresponding sides. For example, if $\frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF}$ , then the sides are proportional and you can use SSS similarity.

What's the difference between congruent and similar triangles?

Congruent triangles are exactly the same size and shape. Similar triangles have the same shape but can be different sizes - their corresponding angles are equal and sides are proportional.

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