J.Byrne 20141. Geometry involves the study of angles, points, lines, surfaces & solids An angle is formed by the intersection of two straight lines. This.

Geometry

Lesson 1

J.Byrne 2014 1

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

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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

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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

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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

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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

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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

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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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Q 4 Redraw the shape below the steps are equally spaced

Q 5 Construct a triangle having a perimeter of 175 with sides in the ratio of 3: 4 : 3

Q 6 Construct a triangle having a perimeter of 175 with sides in the ratio of 4: 2 : 5

Revision Lesson 1

J.Byrne 2014 12