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Geometric Rules and Reasons .pdf


Original filename: Geometric_Rules_and_Reasons.pdf
Title: What fussy Ruth would accept as geometric reasons:
Author: Ministry of Education

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What the Mathematics Department accepts as correct geometric reasons:
1.

adjacent angles on a line add to 180o.

2.

angles at a point add to 360o.

3.

vertically opposite angles are equal.

4.

interior angles of a triangle add to 180o.

5.

base angles of an isosceles triangle are equal.

6.

exterior angle of triangle is equal to the sum of the opposite interior
angles.

7.

corresponding angles on parallel lines are equal.

8.

co-interior angles on parallel lines add to 180o.

9.

alternate angles on parallel lines are equal.

10.

exterior angles of a polygon add to 360o.

11.

interior angles of a polygon add to (n  2) 180 o.
(or interior angles of a pentagon add to 540o….etc).

12.

angle at the centre is equal to twice the angle at the circumference.

13.

angle between a radius and tangent is 90o.

14.

angle in a semicircle is 90o.

15.

angles at the circumference in the same segment (subtended by a chord)
are equal.

16.

opposite angles in a cyclic quadrilateral add to 180o.

17.

exterior angle of a cyclic quadrilateral is equal to the opposite interior
angle.


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