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 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 20142

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° J.Byrne 20143

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 20144

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° 120° B A 55° C J.Byrne 20145

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 20146

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 20147

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. J.Byrne 20148

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 20149

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 J.Byrne

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 J.Byrne

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