Geometry - Georgetown High School



Name___________________________________________ Period _____ Date __________

5-2 Medians and Altitudes of Triangles

A median is a line segment that connects a vertex of a triangle to the midpoint of the opposite side. An altitude of a triangle is a segment from a vertex to the line containing the opposite side meeting at a right angle.

Draw all altitudes in each triangle using a straightedge.

1. 2. 3.

Draw all medians in each triangle using a straightedge.

4. 5. 6.

Draw using a straightedge and label a figure to illustrate each situation.

7. [pic] is a median and an altitude of [pic]

8. [pic] is an altitude of [pic], and [pic] is between [pic] and [pic].

9. [pic] is an angle bisector of [pic], and [pic] is between [pic] and [pic].

10. [pic] is a right triangle with right angle at [pic]. [pic] is a median of [pic]. [pic] is a perpendicular bisector of [pic].

11. Given: [pic] is a median of [pic]

[pic]

Find: [pic]

12. Given: [pic] is an altitude of [pic]

[pic]

Find: [pic]

13. Given: [pic] bisects [pic]

[pic] is an altitude

Prove: [pic] is a median

Statements Reasons

14. Given: [pic] is a median

[pic]

Prove: [pic] bisects [pic]

Statements Reasons

[pic]

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E

D

F

A

B

C

G

I

H

E

D

F

A

B

C

G

I

H

A

D

C

B

B

A

D

C

A

X

C

B

1

2

A

D

C

B

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