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.
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.
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
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
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
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.
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
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
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