basic & secondary parts of triangles.ppt

quiz
1-3. What are angles as
classified according to
the number of congruent
sides.
4-6. What are angles as
classified according to
the measures of their
angles.
7-10. What are the
secondary parts of a
triangle.

Review: Definition
Polygon – a closed
figure made up of many
straight-sided figure.
Copyright © 2000 by Monica Yuskaitis

Definition
Angle – two non-
collinear rays that meet
at a common end point.

Definition
Right Angle – an angle
whose measure is
exactly 90°.Also define
as an angle formed by 2
perpendicular lines.

Definition
Perpendicular lines– are
two lines intersecting at
right angles.
For example,
ray EP & ray ET.
P
E T

Definition
Degree – a unit of
measurement of an angle or
arc, represented by the
symbol º.
30º

Definition
Triangle – a polygon
with 3 angles and 3
straight sides.

EXAMPLE
TRIANGLE
- 3 SIDES.
- 3 VERTICES
- 3 ANGLES

BASIC PARTS
-SIDES
-AS, AM,SM
-VERTICES
-S, A, M
-ANGLES
-S, A. M
S
A
M

TRIANGLES
-ARE NAMED BY
THEIR
VERTICES.
-For example,
-The triangle
shown can be
named as SAM.
S
A
M

SECONDARY PARTS OF A TRIANGLE
Every Triangle has secondary parts

ANGLE BISECTOR
- Is a segment that
DIVIDES (bisects)
any angle of a
triangle into 2
angles of equal
measures.
M N
G S
B
A
AG, BN & SM are angle bisector of BAS.
20°20°
40°
40°
30°
30°

ALTITUDE
-The
height of
a triangle.

ALTITUDE
- It is a segment
drawn from
any vertex of
a triangle
perpendicular
to the
opposite side.
S
C
D
H
N
O

ALTITUDE
EXAMPLE,
SH, NC, OD
are
altitudes of
SON. Copyright © 2000 by Monica Yuskaitis
S
C
D
H
N
O

MEDIAN
NOTE:
like markings
indicates
congruent or
equal parts.
A B
C N
M
O

MEDIAN
THUS, IN THE
FIGURE
OA = MA, OB =
NB, MC = NC.
A B
C N
M
O

A is the
midpoint of MO.
B is the
midpoint of NO
C is the
midpoint of MN
A B
C N
M
O

MEDIAN
- Is a segment drawn
from any vertex of
a triangle to the
MIDPOINT of the
opposite side.
A B
C N
M
O
NA, MB & OC are median of MON.

Property of triangles
The sum of all the angles
equals 180º degrees.
90º 30º
60º

90º 30º
60º
60º
90º
30º
+
180º

90º 50º
40º
40º
90º
50º
+
180º

60º
60º
60º
+
180º
60º 60º
60º

What is the missing angle?
70º
70º
?
+
180º
70º 70º
?
40º

90º
30º
?
+
180º
30º 90º
?
60º

60º
60º
?
+
180º
60º 60º
?
60º

30º
78º
?
+
180º
78º 30º
?
72º

40º
40º
?
+
180º
40º 40º
?
100º

CLASSIFICATION of triangles
ACCORDING TO THE
NUMBER OF CONGRUENT
SIDES.
SCALENE TRIANGLE
- No 2 sides are congruent.
5
8
4
• WHAT CAN YOU SAY ABOUT THE
SIDES OF A TRIANGLE?

ISOCELES TRIANGLE
- 2 sides are congruent.
5
8
5
LEG LEG
VERTEX

PARTS of AN ISOSCELES triangles
5 5
LEGS – are the congruent parts.
Base Angles
VERTEX ANGLE

EQUILATERAL TRIANGLE
- All sides are congruent.
8
8
8
F I
B

ACCORDING TO THEIR
ANGLES.
ACUTE TRIANGLE
- All angles are ACUTE.
85°
40° 55°

ANGLES.
RIGHT TRIANGLE
- One angles is a right angle.
90°
40° 50°

RIGHT TRIANGLE
HYPOTENUSE-
The longest side.
It is the side
opposite the 90º
.
LEGS- are the
other two sides.
leg
leg

ANGLES.
OBTUSE TRIANGLE
- One angle is obtuse.
100°
30° 50°

ANGLES.
EQUIANGULAR TRIANGLE
- All angles are congruent.
60°
60° 60°

 ACCORDING TO
THE NUMBER OF
CONGRUENT
SIDES
 SCALENE
TRIANGLE
 ISOSCELES
TRIANGLE
 EQUILATERAL
TRIANGLE
 ACCORDING TO
THEIR ANGLES
 ACUTE TRIANGLE
 RIGHT TRIANGLE
 OBTUSE
TRIANGLE
 EQUIANGULAR
TRIANGLE

True or false
 1. An isosceles triangle can be an equilateral triangle.
 2. An equilateral triangle can be an isosceles triangle.
 3. A triangle can have two right angles.
 4. An scalene triangle can be an equilateral triangle.
 5. All angles of an equilateral triangle are acute.
 6. All angles of an scalene triangle are acute.
 7. The longest side of a right triangle is called the
vertex.
 8. Base angles of an isosceles triangle are always
acute.
 9. An equiangular triangle is also an equilateral
triangle.
 10. An scalene triangle can be a right triangle.

QUIZ

True or false
 1. A triangle can be isosceles and acute.
 2. A triangle can have two obtuse angles.
 3. A triangle can be obtuse and scalene.
 4. An scalene triangle can be an equilateral
triangle.
 5. A triangle can be right triangle and isosceles.
 6. A triangle can have two right angles.
 7. A triangle can have at most three acute angles.
 8. A triangle can have at least one(1) acute angles.
 9. An equilateral triangle is also an acute triangle.
 10. An equiangular triangle can never be a right
triangle.

NEXT TOPIC
 READ ABOUT
 QUADRILATERALS

basic & secondary parts of triangles.ppt

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basic & secondary parts of triangles.ppt