basic & secondary parts of triangles.ppt

Triangle

1. 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.

2. Triangle
s
LESSON 5

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

4. Definition
Angle –two non-
collinear rays that meet
at a common end point.
Copyright © 2000 by Monica Yuskaitis

5. 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

6. Definition
Perpendicular lines–are
two lines intersecting at
right angles.
For example,
ray EP & ray ET.
Copyright © 2000 by Monica Yuskaitis
P
E T

7. Definition
Degree –a unit of
measurement of an angle or
arc, represented by the
symbol º.
Copyright © 2000 by Monica Yuskaitis
30º

9. Definition
Triangle–a polygon
with 3 angles and 3
straight sides.
Copyright © 2000 by Monica Yuskaitis

10. Copyright © 2000 by Monica Yuskaitis
EXAMPLE
TRIANGLE
-3 SIDES.
-3 VERTICES
-3 ANGLES

11. Copyright © 2000 by Monica Yuskaitis
BASIC PARTS
-SIDES
-AS, AM,SM
-VERTICES
-S, A, M
-ANGLES
-S, A. M
S
A
M

12. Copyright © 2000 by Monica Yuskaitis
TRIANGLES
-ARE NAMED BY
THEIR
VERTICES.
-For example,
-The triangle
shown can be
named as SAM.
S
A
M

13. SECONDARY PARTS OF A TRIANGLE
Copyright © 2000 by Monica Yuskaitis
Every Triangle has secondary parts

14. 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 bisectorof BAS.
20°20°
40°
40°
30°
30°

15. SECONDARY PARTS OF A TRIANGLE
ALTITUDE
-The
heightof
a triangle.
Copyright © 2000 by Monica Yuskaitis

16. 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

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

18. SECONDARY PARTS OF A TRIANGLE
MEDIAN
NOTE:
like markings
indicates
congruent or
equal parts.
Copyright © 2000 by Monica Yuskaitis
A B
C NM
O

19. SECONDARY PARTS OF A TRIANGLE
MEDIAN
THUS, IN THE
FIGURE
OA = MA, OB =
NB, MC = NC.
Copyright © 2000 by Monica Yuskaitis
A B
C NM
O

20. SECONDARY PARTS OF A TRIANGLE
A is the
midpoint of MO.
B is the
midpoint of NO
C is the
midpoint of MN
Copyright © 2000 by Monica Yuskaitis
A B
C NM
O

21. SECONDARY PARTS OF A TRIANGLE
MEDIAN
-Is a segment drawn
from any vertex of
a triangle to the
MIDPOINTof the
opposite side.
Copyright © 2000 by Monica Yuskaitis
A B
C NM
O
NA, MB & OC are median of MON.

22. Copyright © 2000 by Monica Yuskaitis
Property of triangles
The sum of all the angles
equals 180º degrees.
90º30º
60º

23. Copyright © 2000 by Monica Yuskaitis
Property of triangles
The sum of all the angles
equals 180º degrees.
90º30º
60º
60º
90º
30º+
180º

24. Copyright © 2000 by Monica Yuskaitis
Property of triangles
The sum of all the angles
equals 180º degrees.
90º
50º
40º
40º
90º
50º+
180º

25. Copyright © 2000 by Monica Yuskaitis
Property of triangles
The sum of all the angles
equals 180º degrees.
60º
60º
60º+
180º
60º60º
60º

26. Copyright © 2000 by Monica Yuskaitis
What is the missing angle?
70º
70º
?+
180º
70º 70º
?
40º

27. Copyright © 2000 by Monica Yuskaitis
What is the missing angle?
90º
30º
?+
180º30º90º
?
60º

28. Copyright © 2000 by Monica Yuskaitis
What is the missing angle?
60º
60º
?+
180º
60º60º
?60º

29. Copyright © 2000 by Monica Yuskaitis
What is the missing angle?
30º
78º
?+
180º
78º 30º
?
72º

30. Copyright © 2000 by Monica Yuskaitis
What is the missing angle?
40º
40º
?+
180º
40º 40º
?
100º

32. 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?

33. Copyright © 2000 by Monica Yuskaitis
CLASSIFICATION of triangles
ISOCELES TRIANGLE
-2 sides are congruent.
5
8
5
LEG
LEG
VERTEX

34. Copyright © 2000 by Monica Yuskaitis
PARTS of AN ISOSCELES triangles
5 5
LEGS –are the congruent parts.
Base Angles
VERTEX ANGLE

35. Copyright © 2000 by Monica Yuskaitis
CLASSIFICATION of triangles
EQUILATERAL TRIANGLE
-All sides are congruent.
8
8
8
F I
B

36. Copyright © 2000 by Monica Yuskaitis
CLASSIFICATION of triangles
ACCORDING TO THEIR
ANGLES.
ACUTE TRIANGLE
-All angles are ACUTE.
85°
40° 55°

37. Copyright © 2000 by Monica Yuskaitis
CLASSIFICATION of triangles
ACCORDING TO THEIR
ANGLES.
RIGHT TRIANGLE
-One angles is a right angle.
90°
40° 50°

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

39. Copyright © 2000 by Monica Yuskaitis
CLASSIFICATION of triangles
ACCORDING TO THEIR
ANGLES.
OBTUSE TRIANGLE
-One angle is obtuse.
100°
30° 50°

40. Copyright © 2000 by Monica Yuskaitis
CLASSIFICATION of triangles
ACCORDING TO THEIR
ANGLES.
EQUIANGULAR TRIANGLE
-All angles are congruent.
60°
60° 60°

41. 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

42. 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.

43. QUIZ
Copyright © 2000 by Monica Yuskaitis

44. 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.

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