Draw one straight line crossing another straight line Measure all 4 angles C A B D Angle A Angle B Angle C Angle D ID: 248517
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Slide1
Theorems: vertically opposite angles
Draw one straight line crossing another straight line. Measure all 4 angles. C A B D Angle A = Angle B Angle C = Angle DTheorem Vertically opposite angles are equalSlide2
Isosceles triangles
Draw an isosceles triangleTheorem In isosceles triangle the angles opposite the equal sides are equal. Conversely if 2 angles of a triangle are equal the triangle is isosceles.Angle A = Angle B
A BSlide3
Transversals
TheoremIf a transversal makes equal alternate angles on 2 lines the lines are parallel.Conversely if 2 lines are parallel then a transversal makes equal alternate anglesAngle 4 = Angle 6 etc.Slide4
Transversals
TheoremTwo lines are parallel if, and only if, for any transversal the corresponding angles are equal.Eg angle 3 = angle 7(corresponding angles)Slide5
Triangle angles
Draw a triangle.Using your protractor measure all anglesTheoremAll angles of a triangle add up to 180oSlide6
Exterior angles
TheoremThe exterior angle in a triangle is equal to the opposite interior angles.ie angle d = angle a + angle cThe exterior angle is dSlide7
Properties of Parallelograms
Theorem In a parallelogram opposite sides are equal and opposite angles are equal.Conversely if the opposite angles and opposite sides of a quadrilateral are the same the shape is a parallelogram.egSlide8
More properties of Parallelograms
TheoremThe diagonals of a parallelogram bisect each other.Slide9
3 parallel lines
TheoremIf three parallel lines cut off equal segments on some transversal they will cut off equal segments on any other transversal.If lDEl = lFEl
then lCBl = lBA
lSlide10
Triangles
TheoremLet ABC be a triangle. If a line is parallel to BC and cuts AB in a ratio s:t then it also cuts AC in the same ratio. so if lBDl is half the size of lAD
l thenlCEl
is half the size
o
f
l
EA
lThe converse is trueSlide11
More triangles
TheoremIf 2 triangles are similar the their sides are proportional, in order.Slide12
Pythagoras theorem
In a right angled triangle the square of the hypotenuse is the sum of the squares o the other 2 sides.Right angled triangleSlide13
Converse of Pythagoras theorem
TheoremIf the square of one side of a triangle is the sum of the squares on the other 2 sides then the angle opposite the first side is a right angle.Right angled triangleSlide14
Circle
The angle at the centre of a circle standing on a given arc is twice the angle at an point of the circle standing on the same arc.