Synthetic Geometry - Angles

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8 Terms

1
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Vertically opposite angles

  • Vertically opposite angles occur with a X shape

  • They are equal angles

<A = 60°

<ul><li><p>Vertically opposite angles occur with a X shape</p></li><li><p>They are equal angles</p></li></ul><p>&lt;A = 60°</p>
2
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Corresponding angles

  • Corresponding angles exist when you have parallel lines and another line crossing them

  • Parallel lines are 2 lines moving in the same direction that never meet

  • You can spot them with the small arrows pointing in the same direction

  • Corresponding angles form a funny F shape and are always

<B = 110°

<ul><li><p>Corresponding angles exist when you have parallel lines and another line crossing them</p></li><li><p>Parallel lines are 2 lines moving in the same direction that never meet</p></li><li><p>You can spot them with the small arrows pointing in the same direction</p></li><li><p>Corresponding angles form a funny F shape and are always</p></li></ul><p>&lt;B = 110°</p>
3
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Alternate angles

  • Alternate angles exist when you have parallel lines and another line crossing them

  • Alternate angles can be recognised by finding a Z shape between these lines

<C = 120°

<ul><li><p><span>Alternate angles exist when you have parallel lines and another line crossing them</span></p></li><li><p><span>Alternate angles can be recognised by finding a Z shape between these lines</span></p></li></ul><p><span>&lt;C = 120°</span></p>
4
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Congruent triangles

  • In congruent triangles all the angles and all the sides are the same

  • So the 2 triangles are exactly the same

  • It can be tricky to prove for all 3 angles and all 3 sides so there are 4 shortcuts to identify congruency

5
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SSS Side Side Side

All 3 sides are the same

6
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SAS Side Angle Side

when 2 sides and the angle in the middle are the same

7
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ASA Angle Side Angle

when you have 2 angles and the side in the middle are the same

8
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RHS Right Angle Hypotenuse Side

when you have a right angle, the same hypotenuse and one other corresponding side