If $$\theta$$ is the measure of an angle, what is the measure of each angle formed by its bisector?

Each angle formed by the bisector will measure $$\frac{\theta}{2}$$ .

Given that $$\triangle ABC$$ has angle $$\theta$$ , what is the relationship between angles $$\theta$$ and $$\text{CBD}$$ if $$\text{BD}$$ is the angle bisector?

Angle $$\text{CBD}$$ will also measure $$\frac{\theta}{2}$$ .

If angle $$ABC$$ measures 34 degrees, what is the measure of angle $$CBD$$ when $$BD$$ bisects $$\triangle ABC$$ ?

Angle $$CBD$$ measures 34 degrees.

What is the measure of angle $$DBC$$ if angle $$ABC$$ measures 28 degrees and $$BD$$ bisects it?

Angle $$DBC$$ measures 14 degrees.

If $$\text{BD}$$ bisects angle $$ABC$$ and angle $$DBC$$ measures 14 degrees, what is the measure of angle $$DBA$$ ?

Angle $$DBA$$ measures 28 degrees.

How do you find the value of $$x$$ when $$\text{BD}$$ bisects angle $$ABC$$ ?

Set up the equation based on the angle bisector theorem and solve for $$x$$ .

What is the angle bisector theorem?

The angle bisector theorem states that the ratio of the lengths of the two segments created by the bisector is equal to the ratio of the lengths of the other two sides of the triangle.

If $$\text{BD}$$ bisects angle $$ABC$$ and the lengths of sides $$AB$$ and $$AC$$ are known, how can you find the lengths of segments $$AD$$ and $$DC$$ ?

Use the angle bisector theorem to set up a proportion and solve for the lengths.

What is the significance of angle bisectors in triangle geometry?

Angle bisectors help in finding the incenter of a triangle, which is the center of the inscribed circle.

If angle $$ABC$$ measures 60 degrees, what is the measure of each angle formed by the bisector $$BD$$ ?

Each angle will measure 30 degrees.

What is the relationship between the angles formed by an angle bisector and the original angle?

The angles formed by the bisector are equal to half of the original angle.

If $$\text{BD}$$ bisects angle $$ABC$$ and $$\text{AB} = 5$$ and $$\text{AC} = 10$$ , what is the ratio of $$AD$$ to $$DC$$ ?

The ratio of $$AD$$ to $$DC$$ is 1:2.

How can you verify if a line is an angle bisector?

Measure the angles on either side of the line; if they are equal, the line is an angle bisector.

What is the measure of angle $$CBD$$ if angle $$ABC$$ is bisected and measures 80 degrees?

Angle $$CBD$$ measures 40 degrees.

Angle Bisectors Exit Flashcard Flashcards

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1.

FLASHCARD QUESTION

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What is an angle bisector?

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An angle bisector is a line or ray that divides an angle into two equal parts.

2.

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