triangles
TRANSCRIPT
Triangles
LESSON 5
Copyright © 2000 by Monica Yuskaitis
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.
Copyright © 2000 by Monica Yuskaitis
Definition
• Right Angle – an angle whose
measure is exactly 90°.Also define
as an angle formed by 2
perpendicular lines.
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Definition
• Perpendicular lines– are two lines
intersecting at right angles.
• For example,
• ray EP & ray ET.P
E T
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Definition• Degree – a unit of measurement of
an angle or arc, represented by the symbol º.
30º
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Definition
• Triangle – a polygon with 3 angles
and 3 straight sides.
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EXAMPLE
TRIANGLE
- 3 SIDES.
- 3 VERTICES
- 3 ANGLES
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BASIC PARTS -SIDES
-AS, AM,SM
-VERTICES
-S, A, M
-ANGLES
-S, A, M
S
A
M
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TRIANGLES -ARE NAMED BY
THEIR VERTICES.
-For example,
-The triangle
shown can be
named as SAM. S
A
M
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Property of triangles• The sum of all the angles equals
180º degrees.
90º 30º
60º
Copyright © 2000 by Monica Yuskaitis
Property of triangles• The sum of all the angles equals
180º degrees.
90º 30º
60º
60º90º30º+
180º
Copyright © 2000 by Monica Yuskaitis
Property of triangles• The sum of all the angles equals
180º degrees.
90º 50º
40º
40º90º50º+
180º
Copyright © 2000 by Monica Yuskaitis
Property of triangles• The sum of all the angles equals
180º degrees.60º60º60º+
180º60º 60º
60º
Copyright © 2000 by Monica Yuskaitis
What is the missing angle?
70º70º
?+
180º70º 70º
?40º
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What is the missing angle?
90º30º
?+
180º30º 90º
?60º
Copyright © 2000 by Monica Yuskaitis
What is the missing angle?
60º60º
?+
180º60º 60º
?60º
Copyright © 2000 by Monica Yuskaitis
What is the missing angle?
30º78º
?+
180º78º 30º
?72º
Copyright © 2000 by Monica Yuskaitis
What is the missing angle?
40º40º
?+
180º40º 40º
?100º
Copyright © 2000 by Monica Yuskaitis
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?
Copyright © 2000 by Monica Yuskaitis
CLASSIFICATION of triangles
ISOCELES TRIANGLE
- 2 sides are congruent.
5
8
5LEG LEG
VERTEX
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PARTS of AN ISOSCELES triangles
5 5
LEGS – are the congruent parts.
Base Angles
VERTEX ANGLE
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CLASSIFICATION of triangles
EQUILATERAL TRIANGLE
- All sides are congruent.
8
8
8
F I
B
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CLASSIFICATION of triangles
• ACCORDING TO THEIR ANGLES.
ACUTE TRIANGLE
- All angles are ACUTE.
85°
40° 55°
Copyright © 2000 by Monica Yuskaitis
CLASSIFICATION of triangles
• ACCORDING TO THEIR 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
Copyright © 2000 by Monica Yuskaitis
CLASSIFICATION of triangles
• ACCORDING TO THEIR ANGLES.
OBTUSE TRIANGLE
- One angle is obtuse.
100°
30° 50°
Copyright © 2000 by Monica Yuskaitis
CLASSIFICATION of triangles
• ACCORDING TO THEIR ANGLES.
EQUIANGULAR TRIANGLE
- All angles are congruent.
60°
60° 60°
CLASSIFICATION of triangles
• 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
Copyright © 2000 by Monica Yuskaitis
SECONDARY PARTS OF A TRIANGLE
Every Triangle has secondary parts
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SECONDARY PARTS OF A TRIANGLE
• ANGLE BISECTOR
- Is a segment that
DIVIDES (bisects) any
angle of a triangle
into 2 angles of equal
measures.
M N
G SB
A
AG, BN & SM are angle bisector of BAS.
20°20°
40°
40°30°30°
Copyright © 2000 by Monica Yuskaitis
SECONDARY PARTS OF A TRIANGLE
• ALTITUDE
-The height
of a
triangle.
Copyright © 2000 by Monica Yuskaitis
SECONDARY PARTS 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
Copyright © 2000 by Monica Yuskaitis
SECONDARY PARTS OF A TRIANGLE
• ALTITUDE
EXAMPLE,
SH, NC, OD are
altitudes of
SON.S
C
D
H
N
O
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SECONDARY PARTS OF A TRIANGLE
• MEDIAN
NOTE:
like markings
indicates congruent or equal parts.
A B
C NM
O
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SECONDARY PARTS OF A TRIANGLE
• MEDIAN
THUS, IN THE
FIGURE
OA = MA, OB =
NB, MC = NC.
A B
C NM
O
Copyright © 2000 by Monica Yuskaitis
SECONDARY PARTS OF A TRIANGLE
A is the midpoint of MO.
B is the midpoint of NO
C is the midpoint of MN
A B
C NM
O
Copyright © 2000 by Monica Yuskaitis
SECONDARY PARTS OF A TRIANGLE
• MEDIAN
- Is a segment drawn
from any vertex of a
triangle to the
MIDPOINT of the
opposite side.
A B
C NM
O
NA, MB & OC are median of MON.