What is the median, altitude and angle bisector of a triangle?
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What is the median, altitude and angle bisector of a triangle?. Aim:. 2) What is the altitude in miles of the plane in the diagram?. 5 miles. 4 miles. P. A. B. C. Do Now:. 1) What is the median of the numbers –4, -1, 0, 5, 6, 8, 10 ?. Ans: 5. Ans: 3 miles. Def: Median. •. •.

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What is the median, altitude and angle bisector of a triangle?

Aim:

2) What is the altitude in miles of the plane in the diagram?

5 miles

4 miles

P

A

B

C

Do Now:

1) What is the median of the numbers –4, -1, 0, 5, 6, 8, 10 ?

Ans: 5

Ans: 3 miles

Geometry Lesson: Median, Altitude, Angle Bisector


Def median
Def: Median triangle?

F

G

P

Q

L

R

H

E

S

T

V

Def: A median of a triangle is a line segment that joins any vertex of the triangle to the midpoint of the opposite side. Every triangle has three medians.

Examples: Median

In each case below , make a congruence statement about 2 line segments.


Def altitude
Def: Altitude triangle?

3)

B

1)

2)

A

P

K

L

G

A

C

C

B

D

N

B

Def:An altitude of a triangle is a line segment drawn from any vertex of the triangle, perpendicular to and ending on the opposite side. Every triangle has three altitudes.

Examples: Altitude

In each case below, state the name of an altitude and the triangle to which it belongs.

Geometry Lesson: Median, Altitude, Angle Bisector


Def angle bisector
Def: Angle Bisector triangle?

)

)

)

(

)

(

P

(

(

D

L

X

A

Q

Def:An angle bisector of a triangle is a line segment that bisects any angle of the triangle, and terminates on the side opposite the angle. Every triangle has three angle bisectors.

Examples: Angle bisector

Geometry Lesson: Median, Altitude, Angle Bisector


Ex special line segments of triangles
Ex: Special line segments of triangles triangle?

Q

T

T

Q

X

1)

X

P

R

R

P

T

2)

3)

(

(

R

P

X

Geometry Lesson: Median, Altitude, Angle Bisector


Proofs w median altitude angle bisector

B triangle?

C

D

A

Proofs w/Median, Altitude, Angle Bisector

What conclusions can we make based on medians, altitudes and angle bisectors of triangles?

Geometry Lesson: Median, Altitude, Angle Bisector


Proofs w median altitude angle bisector1

1) triangle?Given:

T

Prove:

2) Given:

N

L

X

Prove:

3) Given:

Prove:

Proofs w/Median, Altitude, Angle Bisector

Geometry Lesson: Median, Altitude, Angle Bisector


Proofs w median altitude angle bisector2

4) triangle?Given:

S

R

T

Prove:

N

L

X

Proofs w/Median, Altitude, Angle Bisector

Geometry Lesson: Median, Altitude, Angle Bisector


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