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. Triangles
LESSON 5

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

4. Angle – two non-collinear rays that meet at a common end point.
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.
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6. Perpendicular lines– are two lines intersecting at right angles.
Definition
Perpendicular lines– are two lines intersecting at right angles.
For example,
ray EP & ray ET. P E T
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7. Definition
Degree – a unit of measurement of an angle or arc, represented by the symbol º.
30º
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9. Triangle – a polygon with 3 angles and 3 straight sides.
Definition
Triangle – a polygon with 3 angles and 3 straight sides.
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10. EXAMPLE TRIANGLE 3 SIDES. 3 VERTICES 3 ANGLES
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11. BASIC PARTS S A SIDES AS, AM,SM VERTICES S, A, M ANGLES S, A. M M
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12. Copyright © 2000 by Monica Yuskaitis
TRIANGLES A
ARE NAMED BY THEIR VERTICES.
For example,
The triangle shown can be named as SAM. S M
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13. SECONDARY PARTS OF A TRIANGLE
Every Triangle has secondary parts
Copyright © 2000 by Monica Yuskaitis

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.
20°
20° M N
30°
40°
30°
40° B G S
AG, BN & SM are angle bisector of BAS.

15. SECONDARY PARTS OF A TRIANGLE
ALTITUDE
-The height of 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. H C S N D

17. SECONDARY PARTS OF A TRIANGLE
ALTITUDE
EXAMPLE,
SH, NC, OD are altitudes of
SON. H C S N D
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18. SECONDARY PARTS OF A TRIANGLE
MEDIAN
NOTE:
like markings
indicates congruent or equal parts. A B M C N
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19. SECONDARY PARTS OF A TRIANGLE
MEDIAN
THUS, IN THE FIGURE
OA = MA, OB = NB, MC = NC. A B M C N
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20. 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 M C N
Copyright © 2000 by Monica Yuskaitis

21. 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 M C N
NA, MB & OC are median of MON.
Copyright © 2000 by Monica Yuskaitis

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

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

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

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

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

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

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

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

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

32. CLASSIFICATION of triangles
WHAT CAN YOU SAY ABOUT THE SIDES OF A TRIANGLE?
ACCORDING TO THE NUMBER OF CONGRUENT SIDES. 5 4 8
SCALENE TRIANGLE
- No 2 sides are congruent.
Copyright © 2000 by Monica Yuskaitis

33. CLASSIFICATION of triangles
VERTEX
LEG
LEG 5 5 8
ISOCELES TRIANGLE
- 2 sides are congruent.
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34. PARTS of AN ISOSCELES triangles
LEGS – are the congruent parts.
VERTEX ANGLE 5 5
Base Angles
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35. CLASSIFICATION of trianglesB 8 8 F I 8
EQUILATERAL TRIANGLE
- All sides are congruent.
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36. CLASSIFICATION of triangles
ACCORDING TO THEIR ANGLES.
85°
40°
55°
ACUTE TRIANGLE
- All angles are ACUTE.
Copyright © 2000 by Monica Yuskaitis

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

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

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

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

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.

45. NEXT TOPIC
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QUADRILATERALS