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

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

In triangle ABC, if $$\text{BD}$$ bisects $$\text{angle ABC}$$ , what can be said about the angles formed?

$$m\text{angle ABD} = m\text{angle DBC}$$ .

If $$\text{BD}$$ bisects $$\text{angle ABC}$$ and $$AB = 4$$ and $$AC = 6$$ , what is the ratio of $$\text{AD}$$ to $$\text{DC}$$ ?

The ratio $$\frac{AD}{DC} = \frac{AB}{AC} = \frac{4}{6} = \frac{2}{3}$$ .

If $$\text{QS}$$ bisects $$\text{angle PQR}$$ and $$m\text{angle PQR} = 104\text{°}$$ , what is $$m\text{angle PQS}$$ ?

$$m\text{angle PQS} = \frac{m\text{angle PQR}}{2} = \frac{104\text{°}}{2} = 52\text{°}$$ .

What is the angle bisector theorem?

The angle bisector theorem states that the angle bisector of a triangle divides the opposite side into two segments that are proportional to the lengths of the other two sides.

If $$\text{BD}$$ bisects $$\text{angle ABC}$$ and $$m\text{angle ABD} = 9\text{°}$$ , what is $$m\text{angle DBC}$$ ?

$$m\text{angle DBC} = 9\text{°}$$ .

In a triangle, if $$\text{AB} = 5$$ , $$\text{AC} = 10$$ , and $$\text{AD}$$ is the angle bisector, what is the length of $$\text{DC}$$ if $$\text{BD} = 3$$ ?

Using the angle bisector theorem, $$\frac{AB}{AC} = \frac{BD}{DC}$$ , so $$\frac{5}{10} = \frac{3}{DC}$$ , thus $$DC = 6$$ .

What is the significance of angle bisectors in triangle construction?

Angle bisectors are significant in triangle construction as they help in finding the incenter, which is the center of the inscribed circle.

If $$\text{BD}$$ bisects $$\text{angle ABC}$$ and $$m\text{angle ABC} = 60\text{°}$$ , what is $$m\text{angle ABD}$$ ?

$$m\text{angle ABD} = \frac{60\text{°}}{2} = 30\text{°}$$ .

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

To verify if a line is an angle bisector, check if it divides the angle into two equal angles.

If $$\text{QS}$$ bisects $$\text{angle PQR}$$ and $$m\text{angle PQR} = 80\text{°}$$ , what is $$m\text{angle PQS}$$ ?

$$m\text{angle PQS} = \frac{80\text{°}}{2} = 40\text{°}$$ .

Flashcard

•

Mathematics

•

9th Grade

•

Practice Problem

•

Hard

•

CCSS

HSG.CO.C.9, HSG.C.A.3

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FLASHCARD QUESTION

Front

What is an angle bisector?

Back

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

Tags

CCSS.HSG.CO.C.9

FLASHCARD QUESTION

Front

Back

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSG.CO.C.9

FLASHCARD QUESTION

Front

What is the relationship between the lengths of the segments created by an angle bisector in a triangle?

Back

The angle bisector divides the opposite side into segments that are proportional to the lengths of the other two sides.

Tags

CCSS.HSG.CO.C.9

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSG.CO.C.9

FLASHCARD QUESTION

Front

How do you find the measure of an angle when given its bisector?

Back

To find the measure of an angle when given its bisector, you can use the property that the bisector divides the angle into two equal parts.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSG.CO.C.9

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