If EJ bisects angle DEF, and $$\text{m}\triangle DEJ = 5x + 7$$ and $$\text{m}\triangle JEF = 8x - 8$$ , how do you find x?

Set the two angles equal: $$5x + 7 = 8x - 8$$ , solve for x to get x = 5.

What is the formula to find the measure of an angle when given its bisector?

If $$\text{m}\triangle ABC = x$$ , then the measures of the two angles formed by the bisector are $$\frac{x}{2}$$ each.

How do you determine if a line bisects an angle?

If the two angles formed by the line are equal, then the line bisects the angle.

What is the significance of angle bisectors in triangle geometry?

Angle bisectors are important for finding the incenter of a triangle, which is the point where the angle bisectors intersect.

What is the incenter of a triangle?

The incenter is the point where the angle bisectors of a triangle intersect, and it is equidistant from all sides of the triangle.

How can angle bisectors be used in real-life applications?

Angle bisectors can be used in fields such as architecture, engineering, and design to create symmetrical structures.

What is the relationship between angle bisectors and triangle congruence?

Angle bisectors can help establish congruence in triangles by showing that two angles are equal.

If two angles are bisected, what can be said about the original angles?

The original angles are equal if the bisectors are equal.

Flashcard

•

Mathematics

•

10th Grade

•

Practice Problem

•

Hard

•

CCSS

HSG.CO.C.9, 7.G.B.5, HSG.C.A.3

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15 questions

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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

If a ray bisects an angle, what can be said about the measures of the two angles formed?

Back

The two angles formed are equal in measure.

FLASHCARD QUESTION

Front

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

Back

The sum of the two angles formed by the angle bisector is equal to the measure of the original angle.

Tags

CCSS.HSG.CO.C.9

FLASHCARD QUESTION

Front

If angle DBC measures 14°, what is the measure of angle DBA if DB bisects angle ABC?

Back

28°.

Tags

CCSS.7.G.B.5

FLASHCARD QUESTION

Front

Back

44°.

Tags

CCSS.HSG.CO.C.9

FLASHCARD QUESTION

Front

If angle ABC measures 34°, what is the measure of angle CBD if AB bisects angle ABC?

Back

34°.

Tags

CCSS.7.G.B.5

FLASHCARD QUESTION

Front

Back

22°.

Tags

CCSS.HSG.CO.C.9

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