Midpoint Theorem Summary
Summary - Midpoint Theorem The straight line joining the mid-points of two sides of a triangle is parallel to and equal to half the third side. Converse of mid point theorem - The straight line drawn through the mid point of one side of a triangle, parallel to another,..
Mid - Point Theorem
The straight line joining the mid-points of two sides of a triangle is parallel to and equal to half the third side. P, Q are the mid-points of the sides AB, and AC of (i) PQ || BC (ii) Draw CR || BA to meet PQ produced at ..
The straight line joining the mid-points of two sides of a triangle is parallel to and equal to half the third side. P, Q are the mid-points of the sides AB, and AC of (i) PQ || BC (ii) Draw CR || BA to meet PQ produced at ..Basic Proportionality Theorem
A line parallel to one side of a triangle divides the other two sides into parts of equal proportion. In triangle ABC, a line drawn parallel to BC cuts AB and AC at P and Q respectively. Let the point P divide AB in the ratio of l: m where l and m are natural numbers. Divide AP into 'l' a..
A line parallel to one side of a triangle divides the other two sides into parts of equal proportion. In triangle ABC, a line drawn parallel to BC cuts AB and AC at P and Q respectively. Let the point P divide AB in the ratio of l: m where l and m are natural numbers. Divide AP into 'l' a..Converse of Theorem7
A straight line drawn through the mid-point of one side and parallel to another side of a triangle bisects the third sid..
Converse of Pythagoras' Theorem
If the square on one side of a triangle is equal to the sum of the squares on the other two sides, the angle contained by these two sides is a right angle. In D ABC, if BC 2 = AB 2 + AC 2 then, A is a right ang..
If the square on one side of a triangle is equal to the sum of the squares on the other two sides, the angle contained by these two sides is a right angle. In D ABC, if BC 2 = AB 2 + AC 2 then, A is a right ang..Parallelograms Theorem 3
Statement - A quadrilateral is a parallelogram if one pair of opposite sides are equal and paralle..
Statement - A quadrilateral is a parallelogram if one pair of opposite sides are equal and paralle..Binomial Theorem Summary
Summary - A sentence is called a statement if it can be adjudged as true or false. Every statement is a sentence, but a sentence may or may not be a statement. A statement involving natural number n is generally denoted by P(n). Principle of mathematical induction states that if P(n) is a statement..
Summary - A sentence is called a statement if it can be adjudged as true or false. Every statement is a sentence, but a sentence may or may not be a statement. A statement involving natural number n is generally denoted by P(n). Principle of mathematical induction states that if P(n) is a statement..Area Theorems - Test Questions I
Question 1 - Question: Which of the following equations have x=2, y=3 as solution ? (a) 8x-y = 12 (b) 2x+3y = 10 Answer: (a) Substitute x=2, y=3 in 8x-y=12 8(2)-3=12 16-3=12 x=2, y=3 is not a solution of 8x-y=12 (b) Substitute x=2, y=3 in 2x+3y=10 2(2)+3(3)=10 4+9=10 x=2, y=3 is not a sol..
Question 1 - Question: Which of the following equations have x=2, y=3 as solution ? (a) 8x-y = 12 (b) 2x+3y = 10 Answer: (a) Substitute x=2, y=3 in 8x-y=12 8(2)-3=12 16-3=12 x=2, y=3 is not a solution of 8x-y=12 (b) Substitute x=2, y=3 in 2x+3y=10 2(2)+3(3)=10 4+9=10 x=2, y=3 is not a sol..Midpoint Theorem - Test Questions
Question 1 - Question: Show that the quadrilateral, formed by joining the mid-points of the consecutive sides of a rectangle is a rhombus. Answer: Given: P, Q, R and S are the mid-points of AB, BC, CD and DA respectively. To prove: PQRS is a rhombus. Proof: Consider D BAC ( In a triangle ..
Question 1 - Question: Show that the quadrilateral, formed by joining the mid-points of the consecutive sides of a rectangle is a rhombus. Answer: Given: P, Q, R and S are the mid-points of AB, BC, CD and DA respectively. To prove: PQRS is a rhombus. Proof: Consider D BAC ( In a triangle ..Theorem 5(b):
In a Boolean algebra B, we have 1' ..
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