Angle Comparison in Scalene Triangles: Which is Larger, Angle C or A?

Triangle Angle Relationships with Insufficient Information

ΔABC is a scalene triangle with acute angles.


Which angle is larger,
C ∢C or A ∢A ?

AAABBBCCC

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Step-by-step video solution

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00:00 Which angle is larger - A\C?
00:05 The triangle has acute angles according to the given information
00:10 Because besides this, we are not given any information about the angles
00:15 It cannot be determined
00:19 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

ΔABC is a scalene triangle with acute angles.


Which angle is larger,
C ∢C or A ∢A ?

AAABBBCCC

2

Step-by-step solution

In this problem, we need to determine which angle, C \angle C or A \angle A , is larger in a scalene triangle with acute angles. However, we lack essential information such as specific side lengths or individual angle measurements, which would be necessary to apply triangle inequality or other angle-side relationships. The provided information is not sufficient to definitively compare the angles.

Given that no specific numeric information or other additional data to differentiate the angles is available, there is inherently no possible conclusion.

Therefore, the solution to this problem is: There is no way to know.

3

Final Answer

There is no way to know.

Key Points to Remember

Essential concepts to master this topic
  • Angle-Side Relationship: Larger angles are opposite to longer sides in triangles
  • Information Analysis: Compare given data like side lengths or angle measures
  • Verification: Check if enough specific measurements are provided to make comparison ✓

Common Mistakes

Avoid these frequent errors
  • Assuming angles can be compared without sufficient data
    Don't guess angle relationships based on triangle appearance alone = wrong conclusions! Visual estimates are unreliable and misleading. Always check if specific measurements or relationships are given before making comparisons.

Practice Quiz

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Is the straight line in the figure the height of the triangle?

FAQ

Everything you need to know about this question

Why can't I just look at the triangle and tell which angle is bigger?

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Triangle diagrams can be misleading and not drawn to scale! Without specific measurements like side lengths or angle degrees, you cannot determine which angle is actually larger.

What information would I need to compare the angles?

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You would need either specific angle measurements (like A=45° \angle A = 45° ) or side lengths to use the angle-side relationship: larger angles are opposite longer sides.

Does knowing it's a scalene triangle help?

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A scalene triangle just means all sides are different lengths, so all angles are different too. But this doesn't tell us which specific angle is largest without actual measurements.

What does 'acute angles' tell us about angle comparison?

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Acute angles means all angles are less than 90°, but this doesn't help compare A \angle A and C \angle C specifically. We still need measurements to determine which is larger.

How should I approach problems like this on tests?

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Always list what information you have and what you need. If there's insufficient data to make a definitive comparison, then 'cannot be determined' or 'there is no way to know' is the correct answer!

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