secondary parts of a triangle

SECONDARY PARTS SECONDARY PARTS OF A TRIANGLEOF A TRIANGLE

The The MedianMedian of a triangle of a triangle is a segment whose is a segment whose endpoints are a vertex endpoints are a vertex of the triangle and the of the triangle and the midpoint of the midpoint of the opposite side.opposite side.

AA

X YX Y

M centroidM centroid

B B

Z CZ C

CX, BY, CX, BY, andand AZ AZ are the medians. are the medians.

An An angle bisectorangle bisector of a of a triangle is a segment that triangle is a segment that bisects the angle and bisects the angle and whose endpoints a vertex whose endpoints a vertex of the given angle and a of the given angle and a point on the opposite point on the opposite side.side.

RR

X YX Y

MM

incenterincenter

P Z CP Z C

PY, RZ, & CXPY, RZ, & CX are the angle bisectors are the angle bisectors

An An altitude altitude of a triangle is of a triangle is a perpendicular segment a perpendicular segment from a vertex of a triangle from a vertex of a triangle to the line containing the to the line containing the opposite side.opposite side.

LL

XX

Y Y

M orthocenterM orthocenter

U Z VU Z V

LZ , UX, & VY are the AltitudesLZ , UX, & VY are the Altitudes

AltitudesAltitudes

AA

FF

B C DB C D

EE

PERPENDICULAR BISECTORPERPENDICULAR BISECTOR

of a segment is a segment, of a segment is a segment, ray or line that is ray or line that is perpendicular to the perpendicular to the segment oat its midpoint.segment oat its midpoint.

PP

NN

Y XY X

circumcenter circumcenter MM

Q R Q R

S T US T U

SX, NT,& UYSX, NT,& UY are the perpendicular bisectors are the perpendicular bisectors

Identify the following segments Identify the following segments based on the given figure.based on the given figure.

AA

C C

DD

BB

E GE G

FF

1. AE =1. AE =

2. BG =2. BG =

3. CF =3. CF =

4. ED =4. ED =

5. EG =5. EG =

Draw the following secondary Draw the following secondary parts of the triangle.parts of the triangle.

1.1. Draw a median to AB.Draw a median to AB.

2.2. Draw an altitude to BC.Draw an altitude to BC.

3.3. Draw an angle bisector of B.Draw an angle bisector of B.

4.4. Draw a perpendicular Draw a perpendicular bisector of BCbisector of BC

AA

BB C C

Solve each problemSolve each problem

1.1. In triangle ABC, CX is a median to In triangle ABC, CX is a median to BA. If AB= 15 cm. Find AX.BA. If AB= 15 cm. Find AX.

AA

XX

C C BB

2. 2. In triangle ABC, AY is an angle In triangle ABC, AY is an angle bisector. If m BAY = 36°, find bisector. If m BAY = 36°, find

m BAC. Bm BAC. B

YY

CC

AA

3. 3. Triangle ABC is isosceles with vertex Triangle ABC is isosceles with vertex angle B and BD is an altitude to AC. I angle B and BD is an altitude to AC. I m ABD = 25° ,find m C.m ABD = 25° ,find m C.

BB

AA D D C C

4.Triangle ABC is isosceles with vertex 4.Triangle ABC is isosceles with vertex angle A and AY is an angle bisector.angle A and AY is an angle bisector.

If m BAY = 40°, find m B. If m BAY = 40°, find m B.

A A

B Y CB Y C

5. In triangle ABC, BC AC. 5. In triangle ABC, BC AC.

If m A=42°, find m B.If m A=42°, find m B.

AA

CC B B