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Geometry involves the study of angles, points, lines, surfaces & solids
• An angle is formed by the intersection of two straight lines.
• This angle is called abc with b as the vertex
• If you imagine lines a & b are the hands of a clock and the line a was to move in one complete circle until it was back to its original position. It will have made 1 full revolution.
• A revolution is 360°• Half revolution is 180°• Quarter revolution is 90°
b
a
c
J.Byrne 2014 2
Types of angles
• An acute angle is less than 90°
• A right angle is 90°
• An obtuse angle is more than 90 °
• A reflex angle is greater than 180° but less than 360°
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Types of angles
If two angles add up to 90° they are called complimentary angles
If two angles add up to 180° they are called supplementary angles
If two straight lines are running on the same surface and equal distance apart they are called Parallel lines they will never cross
J.Byrne 2014 4
Transversals & Parallel Lines
• Opposite angles are equal A = B• Corresponding angles are equal A = C
• Find the angles below
• B = 125° A = 125° C = 125°
A
C
B
60°
60°
60°
120°
120°
B
A
55°
C
J.Byrne 2014 5
Bisecting a line
• Draw a line any length call it a,b.
• Set compass to more than half the line length swing an arc above and below the line from both points a & b
• The arcs cross both above and below the line
• Draw a line where the arcs intersect. This line is called the bisector
J.Byrne 2014 6
Bisecting an angle
• Draw an arc from the vertex point b on both lines.
• The arcs intersect at points a & c
• Set the compass again and swing an arc from points a & c
• Draw a line from the vertex to point of intersection.
• This line is called the bisector
J.Byrne 2014 7
Perpendicular & Parallel lines
• Draw a perpendicular line from point P to line ab
• From point P swing an
arc to touch line ab at points 1 & 2
• Swing an arc from points 1 & 2
• Draw a line from point P to point of intersection.
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Dividing Lines
• Divide line ab into 3 equal parts
• Draw a light line any length and angle from point a
• Using a compass step
off 3 times• Join up the last arc to
point b
• Using both set squares
draw lines parallel to last line at each of the arcs
J.Byrne 2014 9
Ratios in Geometry
• Construct a triangle from line ab in the ratio of 2: 3 : 4
• Divide line ac into 9 equal parts
• Draw a parallel line at point 2 & 5
• Line ab is now in the ratio of 2: 3 : 4
• Using side 3 as the base
swing up point a and point b from either corner
• Join up each corner to where the arcs intersect
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Q 1 What are the angles at A,B & C
Q 2 What are the angles at A,B & C
Q 3 Name the angles below
Revision Lesson 1
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