4-7 Medians, Altitudes and Perpendicular bisectors

4-7 Medians, Altitudes and Perpendicular Bisectors

a segment from a vertex of a triangle to the midpoint of the opposite side

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Median:

the perpendicular segments from a vertex to the line that contains the opposite side

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Altitude:

a line (ray or segment) that is perpendicular to the segment at its midpoint.

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Perpendicular Bisector:

If a point lies on the perpendicular bisector of a segment, then the point is equidistant from the endpoints of the segment.

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Theorem 4-5

If a point is equidistant from the endpoints of a segment, then the point lies on the perpendicular bisector of the segment.

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Theorem 4-6

If a point lies on the bisector of an angle, then the point is equidistant from the sides of the angle.

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Theorem 4-7

If a point is equidistant from the sides of an angle, then the point lies on the bisector of then angle,

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Theorem 4-8

Multiple Choice

An altitude is ____ perpendicular to the opposite side.

• Always

• Sometimes

• Never

Multiple Choice

A median is ____ perpendicular to the opposite side.

• Always

• Sometimes

• Never

Multiple Choice

An altitude is ____ an angle bisector.

• Always

• Sometimes

• Never

Multiple Choice

An angle bisector is ____ perpendicular to the opposite side.

• Always

• Sometimes

• Never

Multiple Choice

A perpendicular bisector of a segment is ____ equidistant from the endpoints of the segment.

• Always

• Sometimes

• Never

Open Ended

Suppose $$\overrightarrow{OG}$$ bisects $$\angle\ TOY$$ . What can you deduce if you also know that point J lies on $$\overrightarrow{OG}$$ ?

Open Ended

Suppose $$\overrightarrow{OG}$$ bisects $$\angle\ TOY$$ . What can you deduce if you also know that a point K is such that the distance from K to $$\overrightarrow{OT}$$ is 13 cm and the distance from K to $$\overrightarrow{OY}$$ is 13 cm?