CHAPTER 14 PROBABILITY
CHAPTER 12 SURFACE AREAS AND VOLUMES
Surface area of:
CHAPTER 10 CIRCLES
The collection of all the points in a plane, which are at a fixed distance from a fixed point in the plane, is called a circle. The fixed point is called the centre of the circle.
The fixed distance is called the radius of the circle.
The chord that passes through the centre and joins two points on the circle is called the diameter.
Circumference: The length of the complete circle is called its circumference.
Segment: The region between a chord and either of its arcs is called a segment.
Sector: The region between an arc and the two radii joining the centre to the end points of the arc is called a sector.
CHAPTER 9 AREAS OF PARALLELOGRAMS AND TRIANGLES
CHAPTER 8 QUADRILATERALS
A quadrilateral is a figure having four sides, four angles and four vertices.
ANGLE SUM PROPERTY OF A QUADRILATERAL
This property states that the sum of the angles of a quadrilateral is 360o.
PROPERTIES OF A PARALLELOGRAM
CHAPTER 7 TRIANGLES
CONGRUENCY OF TRIANGLES
The symbol used to represent congruency of two triangles is ≅
1. SAS congruence rule: Two triangles are congruent if two sides and the inclined angle of one triangle are equal to the sides and the included angle of the other triangle.
2. ASA congruence rule: Two triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of other triangle.
3. AAS congruence rule: Two triangles are congruent if any two pair of angles and one pair of corresponding sides are equal.
4. SSS congruence rule: Two triangles are congruent if three sides of one triangle are equal to the three sides of another triangle.
5. RHS congruence rule: Two triangles are congruent if in two right triangles, the hypotenuse and one side of one triangle are equal to the hypotenuse and one side of the other triangle.
Theorems on triangles:
1. Angles opposite to equal sides of an isosceles triangle are equal.
2. The sides opposite to equal angles of triangle are equal.
3. If two sides of a triangle are unequal, the angle opposite to the longer side is larger.
4. In any triangle, the side opposite to the larger angle is longer.
5. The sum of any two sides of a triangle is greater than the third side
CHAPTER 6 LINES AND ANGLES
Line segment: A line segment is a line with two end points.
Ray: A part of the line with one end point is called a ray.
Collinear points: If three or more points lie on the same line, they are called collinear points
Non-collinear points: If three or more points do not lie on the same line they are said to be non-collinear.
Angle: An angle is formed when two rays originate from the same end point.
Arms: The arms of an angle are the rays that make the angle.
Vertex: The end point at which the rays making the angle meet is called the vertex.
TYPES OF ANGLE:
Acute angle: An angle measuring between 0o and 90o is an acute angle.
Right angle: An angle equal to 90o is called a right angle.
Obtuse angle: An angle measuring greater than 90obut less than 180o is called an obtuse angle.
Reflex angle: An angle measuring greater than 1800 but less than 3600 is called a reflex angle.
Complementary angles: Two angles whose sum is 90o are called complementary angles.
Supplementary angles: Two angles whose sum is 180o are called supplementary angles.
AXIOMS AND THEOREMS
Linear pair axioms:
Axiom 1: If a ray stands on a line, then the sum of two adjacent angles so formed is 180o.
Axiom 2: If the sum of two adjacent angles is 180o, then the non-common arms of the angles form a line.
Corresponding angles axiom:
Axiom 3: If a transversal intersects two parallel lines, then each pair of corresponding angles is equal.
Axiom 4: If a transversal intersects two lines such that a pair of corresponding angles is equal, then the two lines are parallel to each other.
CHAPTER 5 INTRODUCTION TO EUCLID’S GEOMETRY
Some of Euclid’s axioms were:
Euclid’s postulates were:
1. A straight line may be drawn from any one point to another point.
2. A terminated line can be produced infinitely.
3. A circle can be drawn with any centre and any radius.
4. All right angles are equal to one another.
5. If a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles, then the two straight lines, if produced indefinitely, meet on that side on which the sum of angles is less than two right angles.