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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