Geometric Bisector Identification: Analyzing Figures with Equal Division

Q: How can I tell if a line is really an angle bisector?

Look for equal angle measures on both sides of the line! In option C, both angles measure 45°, so $ 45° + 45° = 90° $, confirming it bisects the right angle.

Q: Why aren't options A and B correct?

In option A, the angles are 60° and 40° - these are not equal! In option B, the angles are 30° and 33° - also unequal. Only equal angles indicate a true bisector.

Q: Does a bisector always create two 45° angles?

No! The angle measures depend on the original angle. A bisector of a 60° angle creates two 30° angles. A bisector of a 120° angle creates two 60° angles.

Q: Can any angle be bisected?

Yes! Every angle can be bisected, whether it's acute, right, obtuse, or reflex. The bisector always creates two angles that are exactly half the original angle.

Q: What's the difference between a bisector and just any line?

A bisector has a special property: it creates two equal angles. Random lines through an angle usually create unequal angles, so they're not bisectors.

Angle Bisectors with Equal Measure Verification

Which of the following figures has a bisector?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Select the drawing with an angle bisector

00:03 An angle bisector divides the angle into 2 equal parts

00:05 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

Which of the following figures has a bisector?

Step-by-step solution

The answer is C because the angle bisector divides the angle into two equal angles. In diagram C, the angle bisector divides the right angle, which is equal to 90 degrees, into 2 angles that are equal to each other. $45=45$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Definition: Angle bisector divides any angle into two equal parts
Technique: Check if both resulting angles have equal measures like $45° = 45°$
Verification: Add the two equal angles to get the original angle measure ✓

Common Mistakes

Avoid these frequent errors

Confusing any line through an angle with a bisector
Don't assume every line inside an angle is a bisector = wrong identification! A bisector must create exactly equal angles, not just divide the angle. Always check that both resulting angles have identical measures.

Practice Quiz

Test your knowledge with interactive questions

Given:

$∢\text{ABC}=90$

$$ ∢DBC=45 $$

Is BD a bisector?

FAQ

Everything you need to know about this question

How can I tell if a line is really an angle bisector?

Look for equal angle measures on both sides of the line! In option C, both angles measure 45°, so $45° + 45° = 90°$ , confirming it bisects the right angle.

Why aren't options A and B correct?

In option A, the angles are 60° and 40° - these are not equal! In option B, the angles are 30° and 33° - also unequal. Only equal angles indicate a true bisector.

Does a bisector always create two 45° angles?

No! The angle measures depend on the original angle. A bisector of a 60° angle creates two 30° angles. A bisector of a 120° angle creates two 60° angles.

Can any angle be bisected?

Yes! Every angle can be bisected, whether it's acute, right, obtuse, or reflex. The bisector always creates two angles that are exactly half the original angle.

What's the difference between a bisector and just any line?

A bisector has a special property: it creates two equal angles. Random lines through an angle usually create unequal angles, so they're not bisectors.

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