1. MODULE - 7
EUCLIDEAN GEOMETRY

2. Through investigations, produce conjectures and generalizations related to triangles, quadrilaterals and other polygons, and attempt to validate, justify, explain or prove them, using any logical method
(Euclidean, co-ordinate and/or
transformation).
(LO 3 AS 2)

3. Lines and angles Adjacent supplementary angles
In the diagram, angle B one + angle B two = 180 degrees

4. Angles round a point
In the diagram,
a + b + c
= 360 degrees.

5. Vertically opposite angles
Properties:
Vertically opposite angles are equal

6. Corresponding angles If AB//CD, then the
Corresponding angles are equal

7. Alternate angles Properties:
If AB//CD, then the alternate angles are equal.

8. Co – interior angles Properties:
If AB//CD the co – interior angles add up to 180 degrees.

9. TRIANGLES There are four kinds of triangles: Scalene Triangle
Properties:
No sides are equal in length.
Isosceles Triangle
Two sides are equal. Base angles are equal.

10. Equilateral Triangle
All three sides are equal.
All three interior angles are equal
Right-angled triangle
One interior angle is 90 degrees

11. Sum of the angles of a triangle
Exterior angles of a triangle

12. The Theorem of Pythagoras

13. Congruency of triangles
Condition 1:
Two triangles are congruent if three
sides of are triangle are equal in length
to the three sides of the other triangle.

14. Condition 2
Two triangles are congruent if two sides and the included angle are equal to two sides and the included angle of the other triangle.

15. Condition 3
Two triangles are congruent if two angles and one side are equal to two angles and one side of the other triangle.

16. Condition 4
Two right-angled triangles are congruent if the hypotenuse and a side of the one triangle is equal to the hypotenuse and a side of the other
triangle.

17. Similar Triangles
If two triangles are similar (equiangular), then their corresponding sides are in the same
proportion.
If ,then

18. POLYGONS
Definition:
A polygon is a closed figure with three or more sides.
Properties:
The sum of the interior angles of a polygon of n sides is given by the formula:
180° (n - 2).

19. This polygon is called a hexagon. Since there are 6 sides,
Example:
The figure below represents a regular polygon made up of 6 equal sides and 6
equal interior angles.
This polygon is called a hexagon. Since there are 6 sides,
the sum of the interior angles is .

20. The size of the interior angle of a regular
polygon (all sides and interior angle
equal) is given by the formula:
Example
In the previous hexagon, each interior angle (x) is equal to:

21. The sum of the exterior angles of a convex polygon is 360°.
Example
The sum of the exterior angles of the hexagon is 360°

22. Exercise Calculate the size of the angles marked with small letters: X
490 X Y

27. (a) Calculate AC
(b) Calculate
XY.

28. 3. Are the following
pairs of triangles
similar?
(Give a reason for your answer).

29. 4. The two triangles below are similar.
Calculate the value of
x and y.

30. 5. Prove that using two different conditions of congruency.