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Geometry Theorems & Properties Overview

Learn key geometry theorems including properties of angles, triangles, lines, and figures along with their applications. Understand concepts such as perpendicular bisectors, parallel lines, and geometrical relationships in a clear and concise manner.

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Geometry Theorems & Properties Overview

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  1. Theorem 1 Vertically opposite angles are equal in measure <ABC = <EBD & <CBD = <EBA

  2. Theorem 2 In an isosceles triangle, the sides opposite the equal angles are also equal in measure. If <DFE = <DEF, then |DE|= |FD|

  3. Theorem 3 If a transversal makes alternate equal angles on two lines, then the lines are parallel. Converse also true. If <MPO = < LOP, then KL || MG & IF KL || MG then<MPO = < LOP

  4. Theorem 5 Two lines are parallel, if and only if, for any transversal its corresponding angles are equal. Converse also true If KL || MG, then < LOH = <GPH & If < LOH = <GPH, then KL || MG

  5. Theorem 7 <ABC is biggest angle, therefore |AC| is biggest side (opposite each other)

  6. Theorem 8 The length of any two sides added is always bigger than the third side e.g │BC│+ │AB│> │AC│

  7. Theorem 10 The diagonals of a parallelogram bisect each other. i.e│DE│= │EB│ AND │CE│= │EA│

  8. Theorem 15 If the square on one side of a triangle is the sum of the squares on the other two, then the angle opposite first side is 90o i.e. If │AC│2= │AB│2+│BC│2 then <CBA =90o

  9. Theorem 16 For a triangle, base times height does not depend on choice of base Area of Triangle = ½ base x height Therefore: ½ |AC| x |FB|= ½ |AB| x |DC|

  10. Theorem 17 The diagonal of a parallelogram bisects its area i.e. Area of Triangle ABC = ½ │AB│ x h Area of Triangle ADC= ½ │CD│ x h Since |AB|=|CD|; Area of both triangles are the same

  11. Theorem 18 The area of a parallelogram is base by height i.e. Area of Triangle ABC = ½ │AB│ x h and Area of Triangle ADC= ½ │CD│ x h. Since |AB|=|CD| Area of Parallelogram = 2 (½ │AB│ x h) = │AB│ x h (i.e Base x Height)

  12. Theorem 20 Each tangent is perpendicular to the radius that goes to the point of contact |AP|┴ |PC|……… where P is the point of contact

  13. Theorem 21 The perpendicular from the centre to a chord bisects the chord. The perpendicular bisector of a chord passes though the centre. If |AE| ┴|CD| Then.. |CE| = |ED|

  14. Corollary 6 If two circles share a common tangent line at one point, then two centres and that point are co-linear • • • • • • • Co-linear – along the same line

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