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### Geometry2.17 Triangles And Polygons Review

1. The sum of the three angles of a triangle is 1800.

2. If one side of a triangle is produced the exterior angle formed is equal to the sum of the interior opposite angle.Ā The exterior angle is greater than each of the interior opposite angles.

3. Triangle: A closed place figure of three sides is called a triangle.

4. Quadrilateral: A closed plane figure of four sides is called a quadrilateral.

5. Pentagon: A closed plane figure of five sides is called a pentagon.

6. Hexagon: A closed plane figure of six sides is called a hexagon.

7. Polygon: A closed plane figure of many sides is called polygon.

8. Convex polygon: If each of the angles of a polygon is less than 1800, it is called a convex polygon.

9.Concave polygon: If atleast one angle of a polygon is greater than 1800, it is called a concave polygon.

10. Regular polygon: The polygon in which all the sides are of equal length is called a regular polygon.Ā All the angles of a regular polygon are equal.

11. The sum of the exterior angles of a polygon is equal to four right angles.

12. The sum of the interior angles of a polygon of 'n' sides is equal to (n-2)180 or (2n-4)rt. angles.

 Polygon Number of sides Sum of Interior angles: (n-2)180 Sum of exterior angles Triangle 3 180 360 Quadrilateral 4 360 360 Pentagon 5 540 360 Hexagon 6 720 360 Heptagon 7 900 360 Octagon 8 1080 360 Nonagon 9 1260 360 Decagon 10 1440 360

13. In a regular polygon of 'n' sides,
i) Each exterior angle = 360/n.
ii) Each interior angle = 1800 - Exterior angle.
iii) No. of sides = 360/Exterior angle.

14. Two geometrical figures are said to be congruent if they have the same shape and same size.

15. Two triangles are congruent if,
i) The three sides of one are equal to the three sides of the other. (SSS Axiom)
ii) Two sides and included angle of one are equal to two sides and included angle of the other. (SAS Axiom)
iii) If any two angles and the included side of one are equal to two angles and the included side of the other. (ASA Axiom)
iv) Two right angled triangles are congruent if and only if the hypotenuse and a side of one triangle are equal to the hypotenuse and the corresponding side of the other. (RHS Axiom)

16. In an isosceles triangle the angles opposite to congruent sides are congruent.

17. In an isosceles triangle the sides opposite to congruent angles are congruent.

18. In an equilateral triangle all the three angles are congruent and each is 600.

19. In a triangle if two sides are unequal the angle opposite to longer side is greater than the angle opposite to the shorter side.

20. In a triangle if two angle are unequal, the side opposite to greater angle is longer than the side opposite to smaller angle.

21.The sum of any two sides of a triangle is greater than the third side.

22.Ā Of all the line segments drawn to a given line from a given point not on it, the perpendicular is the shortest.

23. In a right angle triangle the hypotenuse is greater than each of the other two sides.