Identifying Base Angles in Isosceles Triangles: Key Properties and Relationships

Triangle Classification with Angle-Side Relationships

In an isosceles triangle, the angle between ? and ? is the "base angle".

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Step-by-step written solution

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1

Understand the problem

In an isosceles triangle, the angle between ? and ? is the "base angle".

2

Step-by-step solution

An isosceles triangle is one that has at least two sides of equal length. The angles opposite these two sides are known as the "base angles."
The side that is not equal to the other two is referred to as the "base" of the triangle. Thus, the "base angles" are the angles between each of the sides that are equal in length and the base.
Therefore, when we specify the angle in terms of its location or position, it is the angle between a "side" and the "base." This leads to the conclusion that the angle between the side and the base is the "base angle."

Therefore, the correct choice is Side, base.

3

Final Answer

Side, base.

Key Points to Remember

Essential concepts to master this topic
  • Definition: Base angles are opposite the two equal sides
  • Technique: Equal sides create equal base angles at triangle base
  • Check: Both base angles measure the same degrees ✓

Common Mistakes

Avoid these frequent errors
  • Confusing vertex angle with base angles
    Don't call the angle between the two equal sides a 'base angle' = wrong terminology! The vertex angle is at the top, between equal sides. Always remember base angles are where equal sides meet the base.

Practice Quiz

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Is the triangle in the drawing a right triangle?

FAQ

Everything you need to know about this question

What exactly is the 'base' of an isosceles triangle?

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The base is the side that's different from the other two equal sides. It's usually drawn at the bottom, but any side can be the base as long as it's the unequal one!

Are base angles always equal in isosceles triangles?

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Yes! Since the two sides touching the base are equal in length, the angles they make with the base must also be equal. This is a fundamental property of isosceles triangles.

How many base angles does an isosceles triangle have?

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Every isosceles triangle has exactly two base angles. They're located where each of the equal sides meets the base of the triangle.

What's the difference between base angles and vertex angle?

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The vertex angle is at the top, between the two equal sides. The base angles are at the bottom corners, where the equal sides meet the base. There's 1 vertex angle and 2 base angles.

Can I identify base angles if the triangle is rotated?

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Absolutely! Base angles are defined by their relationship to the sides, not their position. Look for the two angles opposite the equal sides, regardless of how the triangle is oriented.

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