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?

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

If $$\text{AB} = 10$$ and $$\text{AC} = 15$$ , and $$\text{BD}$$ bisects $$\text{angle ABC}$$ , what is the ratio of $$\text{AD}$$ to $$\text{DC}$$ ?

The ratio $$\frac{\text{AD}}{\text{DC}} = \frac{10}{15} = \frac{2}{3}$$ .

How do you find the value of $$x$$ when given an angle bisector problem?

Set up an equation based on the properties of angle bisectors and solve for $$x$$ .

If $$\text{RQ}$$ bisects $$\text{angle PRS}$$ and $$\text{angle PRQ} = 30^\text{o}$$ , what is $$\text{angle QRS}$$ ?

$$\text{angle QRS} = 30^\text{o}$$ .

In a triangle, if $$\text{BD}$$ bisects $$\text{angle ABC}$$ and $$\text{angle ABD} = 40^\text{o}$$ , what is $$\text{angle DBC}$$ ?

$$\text{angle DBC} = 40^\text{o}$$ .

What is the formula to calculate the angles when an angle bisector is involved?

Use the property that $$\text{angle ABD} = \text{angle DBC}$$ .

If $$\text{BD}$$ bisects $$\text{angle ABC}$$ and $$\text{angle ABC} = 80^\text{o}$$ , what are the measures of $$\text{angle ABD}$$ and $$\text{angle DBC}$$ ?

$$\text{angle ABD} = \text{angle DBC} = 40^\text{o}$$ .

What is the significance of angle bisectors in triangle construction?

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

What is the relationship between angle bisectors and the incenter of a triangle?

The incenter is the point where the angle bisectors of a triangle intersect.

If $$\text{BD}$$ bisects $$\text{angle ABC}$$ and $$\text{angle ABC} = 90^\text{o}$$ , what are the measures of the angles formed?

$$\text{angle ABD} = \text{angle DBC} = 45^\text{o}$$ .

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

Back

Tags

CCSS.HSG.CO.C.9

FLASHCARD QUESTION

Front

What is the Angle Bisector Theorem?

Back

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.

Tags

CCSS.HSG.CO.C.9

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