solving basic geometry definitions

Introduction - We have studied so far about equalities in a triangle. In an isosceles triangle two of the sides are equal. In an equilateral triangle all the sides are equal. But there exist several situations where we need to compare quantities which are not equal. This gives rise to the concept o..

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, bisects the third side. The I..

Then (x 1 , y 1 ) lies on both (i) and (ii). Solving for x 1 and y 1 by the method of cross multiplication, we obtain ..

Question: Prove the converse of mid-point theorem using Basic Proportionality Theorem. That is, prove that the line drawn from the mid-point of one side of a triangle, parallel to the second side, bisects the third side. [2 Mark] Answer: Given: ABC is a triangle where AD ..

Question 1 - Question: Answer: Line through the origin and perpendicular to x + y - 4 = 0 is x - y = 0 ...(iv) \ The foot of the perpendicular is given by solving (i) and (iv), x = y = 2. (2,2) are the coordinates of the foot of the perpendicular. Line through the origin perpendicular to ..

Question: Solve the following equation: 7x+5=3x-25 Answer: ..

Question: Solve the following equation: Answer: 2y-15=180 2y=180+15 2y=195 ..

Question: Solve graphically x - 2y = 1 and x + y = 4. Use 2cm = 1 unit on both axes and plot only 3 points per line. Answer: x - 2y = 1 2y = x - 1 x + y = 4 y = 4 - x ..

Question: Solve the following equation: Answer: 5(2-9x) = 4(15-4x) (by cross multiplication) 10-45 x= 60-16x -45x+16x=60-10 -29x=50 ..

Question: Solve the following equation: Answer: 4x + 7 = -3 (2x + 1) (By cross-multiplication) 4x+7=-6x-3 4x+6x=-3-7 10x=-10 x=-..