the radius of curvature of curve y=f(x) at any point on curve is
Answers
Step-by-step explanation:
real numbers, plotting them and showing that they lie on a line. Graph of linear equations in two variables Examples problems from real life, including problems on Ratio and Proportion and with algebraic and graphical solutions being done simultaneously
UNIT III: COORDINATE GEOMETRY
Coordinate Geometry
(6 Periods)
The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations, plotting points in the plane
UNIT IV: GEOMETRY
1. Introduction to Euclid's Geometry (Not for assessment)
(6 Periods)
History- Geometry in India and Euclid's geometry Euclid's method of formalizing observed phenomenon into rigorous Mathematics with definitions, common/obvious notions axioms/postulates and theorems The five postulates of Euclid. Equivalent versions of the fifth postulate. Showing the relationship between axiom and theorem, for example:
(Axiom) 1. Given two distinct points, there exists one and only one line through them. (Theorem) 2. (Prove) Two distinct lines cannot have more than one point in common
2. Lines and Angles
(13 Periods)
1. (Motivate) If a ray stands on a line then the sum of the two adjacent angles so formed is 180 and the converse
2 (Prove) If two lines intersect, vertically opposite angles are equal 3. (Motivate) Results on correspondi transversal intersects two parallel lines angles, alternate angles, interior angles when a
4. (Motivate) Lines which are parallel to a given line are parallel 5. (Prove) The sum of the angles of a triangle is 180.
6. (Motivate) If a side of a triangle is produced, the exterior angle so formed is equal to the sum of the two interior opposite angles
3. Triangles
(20 Periods)
1. (Motivate) Two triangles are congruent if any two sides and the included angle of one triangle is equal to any two sides and the included angle of the other triangle (SAS Congruence)
2. (Prove) Two triangles are congruent if any two angles and the included side of one triangle is equal to any two angles and the included side of the other triangle (ASA
Congruence)
3. (Motivate) Two triangles are congruent if the three sides of one triangle are equal to three sides of the other triangle (SSS Congruence). 4. (Motivate) Two right triangles are congruent if the hypotenuse and a side of one
triangle are equal (respectively) to the hypotenuse and a side of the other triangle.
(RHS Congruence)
5. (Prove) The angles opposite to equal sides of a triangle are equal 6. (Motivate) The sides opposite to equal angles of a triangle are equal
7. (Motivate) Triangle inequalities and relation between 'angle and facing side' inequalities in triangles.
4. Quadrilaterals
(10 Periods)
1. (Prove) The diagonal divides a parallelogram into two congruent triangles. 2. (Motivate) In a parallelogram opposite sides are equal, and conversely,
3. (Motivate) In a parallelogram opposite angles are equal, and conversely. 4. (Motivate) A quadrilateral is a parallelogram if a pair of its opposite sides is parallel
and equal
5. (Motivate) In a parallelogram, the diagonals bisect each other and conversely 6. (Motivate) In a triangle, the line segment joining the mid-points of any two sides is parallel to the third side and is half of it and (motivate) its converse