If $$AB = 10$$ and $$AC = 15$$ , what is the ratio of $$BD$$ to $$DC$$ if $$D$$ is on the angle bisector of $$\triangle ABC$$ ?

The ratio $$\frac{BD}{DC} = \frac{AB}{AC} = \frac{10}{15} = \frac{2}{3}$$ .

If $$\triangle ABC$$ has $$\theta = 80^\text{o}$$ , what are the measures of $$\triangle ABD$$ and $$\triangle ACD$$ if $$AD$$ is the angle bisector?

Both angles $$\triangle ABD$$ and $$\triangle ACD$$ measure $$40^\text{o}$$ .

What is the significance of the point where the perpendicular bisector intersects a segment?

The intersection point is the midpoint of the segment, and it is equidistant from both endpoints.

If $$\triangle ABC$$ has sides $$AB = 8$$ and $$AC = 6$$ , what is the length of $$BD$$ if $$D$$ is on the angle bisector of $$\triangle ABC$$ ?

Using the Angle Bisector Theorem, $$BD = \frac{8}{8+6} \times DC$$ .

How can you verify if a point lies on the perpendicular bisector of a segment?

To verify, measure the distances from the point to each endpoint of the segment; if the distances are equal, the point lies on the perpendicular bisector.

What is the formula for finding the length of a segment using the coordinates of its endpoints?

The length of a segment with endpoints $$(x_1, y_1)$$ and $$(x_2, y_2)$$ is given by $$\text{Length} = \text{sqrt}((x_2 - x_1)^2 + (y_2 - y_1)^2)$$ .

If $$\triangle ABC$$ has angles $$\theta_1 = 30^\text{o}$$ and $$\theta_2 = 60^\text{o}$$ , what is the measure of $$\theta_3$$ ?

Using the triangle sum theorem, $$\theta_3 = 180^\text{o} - (30^\text{o} + 60^\text{o}) = 90^\text{o}$$ .

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

The lengths of the segments created by an angle bisector are proportional to the lengths of the other two sides of the triangle.

If $$\triangle ABC$$ is isosceles with $$AB = AC$$ , what can be said about the angles opposite these sides?

The angles opposite the equal sides are also equal.

Perpendicular Bisector and Angle Bisector Theorem Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is a perpendicular bisector?

Back

A perpendicular bisector is a line that divides a line segment into two equal parts at a 90-degree angle.

2.

FLASHCARD QUESTION

Front

State the Perpendicular Bisector Theorem.

Back

The Perpendicular Bisector Theorem states that any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment.

Tags

CCSS.HSG.CO.C.9

3.

FLASHCARD QUESTION

Front

What is an angle bisector?

Back

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

Tags

CCSS.HSG.CO.C.9

4.

FLASHCARD QUESTION

Front

State the Angle Bisector Theorem.

Back

The Angle Bisector Theorem states that the ratio of the lengths of the two segments created by an angle bisector on the opposite side is equal to the ratio of the lengths of the other two sides of the triangle.

Tags

CCSS.HSG.CO.C.9

5.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSG.CO.C.9

6.

FLASHCARD QUESTION

Front

How do you find the length of a segment using the Perpendicular Bisector Theorem?

Back

To find the length of a segment using the Perpendicular Bisector Theorem, measure the distance from any point on the bisector to each endpoint of the segment; these distances will be equal.

Tags

CCSS.HSG.CO.C.9

7.

FLASHCARD QUESTION

Front

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

Back

Tags

CCSS.HSG.CO.C.9

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