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Geometry
Facts about lines and triangles
Vertically opposite angles are equal in measure
Straight line adds to 180°
A+B=180°
Alternate angles are equal in measure
(when you have 2 parallel lines and line
going through them-angles inside lines)
Corresponding angles are equal in measure
(they are on the top of parallel lines or on the bottom
either side)
Angles in a triangle add to 180°
The exterior angle of a triangle is equal to the 2
interior opposite angles
<x=<a+<b
If 2 sides of a triangle are equal in measure the angles opposite those
sides are equal in measure called isosceles triangle.
In an equilateral triangle all the sides are equal all the angles are
equal to 60°.
Facts about parallelograms
Opposite angles and sides in a parallelogram are equal in
measure.
Adjacent angles add to 180°
< A + < D = 180°
<B + < C =180°
When a diagonal is drawn, alternate angles are equal. The
diagonal does not bisect the corner angles.
A=C B=D
A
D
C
D
Facts about Circles
The measure of the angle at the centre standing on the arc is twice the
measure of the angle at the circumference, standing on the same arc.
All angles at the circumference standing on the same arc are
equal in measure.
The angle at the circumference standing on the diameter is 90°.
Angle opposite centre is 90°.
Revision of Geometry 1 and 2
Similar Triangles have the same angels and can be put as fraction in same ratio
Similar Triangles
Circle Question
To prove Congruency by 4 methods
SSS- Side, Side, Side
ASA- Angle, Side, Angle
SAS- Side, Angle, Side
RHS - Right angle, Hypotenuse, Side
Example
Example
Pythagoras theorem
h2=a2+b2
H
A
hyp2 = sum of the other 2 sides squared
b
Example
Find b?
1
2
b
h2=a2+b2
22 = 12 +b2
4 = 1 + b2
4-1 = b2
3 = b2
√3 = b
Example of Pythagoras theorem
hyp is always opposite right angle
x2 = 8 2 + 6 2
x2 = 100
x = 10
Get x 1st
Square root 100 to get rid of square
262 = 102 + y2
y2 = 576
y = 24
when you get x sub back in to find y
Square root 576 to get rid of square