triangles

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.

Copyright © 2000 by Monica Yuskaitis

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

Copyright © 2000 by Monica Yuskaitis

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

Copyright © 2000 by Monica Yuskaitis

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

Copyright © 2000 by Monica Yuskaitis

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.