Angles can be acute (less than 90 degrees), right (90 degrees), obtuse (between 90-180 degrees), or reflex (greater than 180 degrees). Triangles are classified based on their sides and angles, and always sum to 180 degrees. Circles are sets of points equidistant from a center, with properties like radius, diameter, and circumference. Parallel lines have the same distance between them and never intersect, forming corresponding, alternate interior, alternate exterior, and consecutive interior angles of equal measure when cut by a transversal.

1.  Angles  Triangles
 Circles
 Parallelism

2. ANGLES
Ananglemeasurestheamountofturn

3. What isan angle?
• Two raysthat share the same endpoint form an angle. The point where the rays
intersect is called the vertexof the angle.The two rays arecalled the sides of the
angle.

4. Here aresome examples
ofangles.

5. • Wecan identify an angle by using a point oneach ray and the vertex.The angle
belowmay be identified as angle ABC oras angle CBA. Thevertexpoint is always
in themiddle.
A
C
B
LabellingAngles

6. • Wecan also identify an angle by giving the angle a name, usually a lower-case letter
like a or b, orsometimes a Greek letter like α (alpha) orθ(theta).
LabellingAngles

7. • Wemeasure the size of an angle using degrees.
• Here aresome examplesof angles and their degreemeasurements.
AngleMeasurements

8. • An acute angle is an angle measuring between 0 and 90 degrees.
• Thefollowing angles are all acute angles.
AcuteAngles

9. • A right angle is an angle measuring exactly 90 degrees (¼ rotation).
• Thefollowing angles are both right angles.
Right Angles

10. • An obtuse angle is an angle measuring between 90 and 180 degrees.
• Thefollowing angles are all obtuse angles.
Obtuse Angles

11. • A straight angle is an angle measuring exactly 180 degrees (½ rotation).
StraightAngle

12. • A reflex angle is an angle measuring between 180 and 360 degrees.
• Thefollowing angles are all reflex angles.
ReflexAngle

13. • Its angle measuresexactly 360 degrees.
Full Rotation

14. • In one diagram
Angles

15. Be careful whatyou measure
This is an This is a reflex angle.
obtuse angle.
Angles

16. TRIANGLES
Anglesinatriangle always addto180degrees

17. What is atriangle?
• A triangle is a polygon with three cornersand three sides. The three corners are
called vertices and the three sides are also called edges which areline segments.

18. 1. By their sides
• EquilateralTriangle
• Isosceles Triangle
• ScaleneTriangle
Classifying Triangles
2. By their angles
• AcuteTriangle
• RightTriangle
• ObtuseTriangle

19. • Threeequal sides
• Threeequal angles
EquilateralTriangle

20. • Twoequal sides
• Twoequal angles
IsoscelesTriangle

21. • Noequal sides
• Noequal angles
ScaleneTriangle

22. • An acute angle has threeacute angles
AcuteTriangle

23. • A right triangle has oneright angle.
Right Triangles

24. • An obtuse triangle has one obtuse angle.
Obtuse Triangle

25. • Sometimes a triangle will have two names
Combining the Names
RightScaleneTriangle
Onerightangle
Two otherunequal angles
Noequalsides

26. • Sometimes a triangle will have two names
Combining the Names
RightIsosceles Triangle
Onerightangle
Two otherequal angles(alwaysof45degrees)
Two equalsides

27. • Sometimes a triangle will have two names
Combining the Names
ObtuseIsosceles Triangle

28. • Sometimes a triangle will have two names
Combining the Names
AcuteScaleneTriangle

29. • Sometimes a triangle will have two names
Combining the Names
AcuteIsosceles Triangle

30. • Sometimes a triangle will have two names
Combining the Names
ObtuseScaleneTriangle

31. • Sometimes a triangle will have two names
Combining the Names
RightIsosceles Triangle

32. CIRCLES
Acircleisasimpleclosedcurvewhich dividestheplaneintotwo
regions:aninteriorandanexterior.

33. What is acircle?
• A circleis the set of all points on a plane that are a fixed distance from a center.

34. Radius,Diameterand Circumference
• Thefixed distance from a centeris called the radius.A line through the center that
divides the circlein half is called the diameter. The circumferenceis the distance
around the edge of the circle.

35. Radius,Diameterand Circumference
𝐶𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒
𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟
= 𝜋 = 3.14159
Therefore,
Circumference = 𝜋 × 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟
Thus,
𝐶𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = 2 × 𝜋 × 𝑅𝑎𝑑𝑖𝑢𝑠

36. • A line that goes from onepoint to another on the circle’s circumference is called a
chord.If that line passes through the center, it is called a diameter. Atangent is a
line that “just touches” the circle onceas it passes and secantif it touches twice.
Lastly, a part of a circumference is called an arc.
Lines

37. Lines

38. • There aretwo main “slices” of a cicle.
• The“pizza” slice is called a sector and the slice made bya chordis called
a segment.
Slices

39. • There aretwo types of sector.
• Quarter of a circle is called a quadrant.
• Half a circle is called a semicirle.
CommonSector
Quadrant

40. PARALLELISM
Always thesamedistance apartandnevertouching

41. • Lines are parallel if they are always the same distance apart(called equidistant ),
and will nevermeet.
• Parallel lines also point in the same direction
;
Example A Example B
ParallelLines

42. • When parallel lines get crossedby another line (which is called a traversal),you
can see many angles arethe same.
• These angles can be made into pair ofangles which
have special names
Pairsof Angles

43. • Vertical Angles
• Corresponding Angles
• Alternate Interior Angles
• Alternate Exterior Angles
• Consecutive Interior Angle
Pairsof Angles

44. • Thevertical angles are the angles opposite each other when two line cross
• “Vertical” in this case means that they share the same vertex
VerticalAngles

45. • When two lines arecrossed by a traversal,the angles in matching corners are
called correspondingangles
CorrespondingAngles

46. • When two lines arecrossed by a traversal,the pairs of angles onopposite sides of
the transversal but inside the two lines arecalled alternate interior angles
AlternateInteriorAngles

47. • When two lines arecrossed by a traversal,the pairs of angles onopposite sides of
the transversal but outside the two lines are called alternate exterior angles
AlternateExterior Angles

48. • When two lines arecrossed by a traversal,the pairs of angles onone side of the
transversal but inside of the two lines arecalled consecutiveinterior angles
ConsecutiveInterior Angles

49. • Someof those special pair ofangles can be used to test if lines really are parallel:
• If anypair of
– CorrespondingAngles areequal
– AlternateInteriorAngles areequal
– AlternateExteriorAngles areequal
– ConsecutiveInteriorAngles areequal
Thenthe lines areparallel.
Testing for ParallelLines

50. • Powerpoint template –www.fppt.info
• Main Contexts - www.mathsisfun.com
o SubContexts- en.wikipedia.org
Sources