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HOW TO THINK ABOUT

HOW TO THINK ABOUT. GEOMETRY 1. JW Hick. When naming an angle, the middle letter is the vertex. This angle is called angle CAB. ANGLE CLASSIFICATIONS Acute angle – less than 90 degrees Right angle – 90 degrees Obtuse angle – Between 90 and 180 degrees

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HOW TO THINK ABOUT

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  1. HOW TO THINK ABOUT GEOMETRY 1 JW Hick

  2. When naming an angle, the middle letter is the vertex. This angle is called angle CAB

  3. ANGLE CLASSIFICATIONS Acute angle – less than 90 degrees Right angle – 90 degrees Obtuse angle – Between 90 and 180 degrees Reflex angle – Between 180 and 360 degrees Revolution – 360 degrees

  4. Complementary angles add up to 90 degrees Supplementary angles add up to 180 degrees Adjacent angles are next to each other A right angles is 90 degrees

  5. TRIANGLE CLASSIFICATION Triangles can be classified by their angles and their side lengths. An acute angle triangle has all 3 angles less than 90 degrees. An obtuse triangle has one obtuse angle A right angled triangle has one right angle

  6. A scalene triangle has all three sides different lengths An isosceles triangle has two sides the same length as each other An equilateral triangle has all three sides the same length

  7. EXAMPLE: Name the following triangle according to its properties This triangle has one obtuse angle, and two sides the same length as each other. Hence it is an “obtuse angled isosceles triangle”

  8. OTHER POLYGONS A parallelogram is a 4 sided shape (quadrilateral) which has two pairs of parallel sides. Opposite sides and opposite angles are equal in parallelograms, and the diagonals bisect each other (cut each other in half). Examples of parallelograms include squares, rectangles and rhombuses

  9. Parallelogram Trapezium Kite

  10. PARALLEL LINE THEOREMS Alternate angles are equal on parallel lines (Z shaped)

  11. Corresponding angles are equal on parallel lines (F shaped)

  12. Cointerior angles are supplementary (add to 180) on parallel lines (C shaped)

  13. EXAMPLE Find the value of all thetas in the following.

  14. Well, forms a Z shape with our 130 degree angle, so they are both equal then, hence is 130 degrees due to alternate angles. forms a C shape, known as corresponding angles, so these add to 180 degrees. Hence is 50 degrees. The final angle forms an F shape with our 130 degree angle. This is known as a corresponding angle, hence equals 130 degrees

  15. NOTE: These angles Z, C and F shaped can all be rotated around and reflected and they still hold true. For example imagine a C facing the wrong way. This is still a cointerior angle.

  16. ANGLE PROPERTIES Angles next to each other (adjacent) on a straight line will add to 180 degrees

  17. Angles next to each other at a point will add to 360 degrees (as there is 360 degrees in a circle) Vertically opposite angles are equal to each other.

  18. EXAMPLE Find the value of theta and alpha

  19. ANGLE SUM OF POLYGONS To find the interior angle sum of any polygon (what they all add up to) you see how many sides the shape has, subtract two from this number and multiply your answer by 180. Example: A 5 sided shape (pentagon) would have an interior angle sum of 3 x 180 = 540 degrees

  20. A polygon is called “regular” if all the sides are equal length, and all the angles are the same size. The exterior angle sum of any polygon is 360 degrees. All 5 of these angles will add to 360 degrees.

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