secondary parts of a triangle
TRANSCRIPT
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