ratio theorem

The medians of a triangle pass through the same point which divides each of the medians in the ratio 2:..

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..

Let \ AB = BC = a Using Pythagoras Theorem AC 2 = a 2 + a 2 = 2a 2 ..

Divide AB = 8.4 cm internally in the ratio of 3 : 2. 1. Draw AB = 8.4 cm and through A draw another line AX at an acute angle to AB. 2. Make ABY = BAX so that BY is on the opposite side of AB to that of AX. 3. With suitable radius, cut off equal lengths AH, HJ, JK, KL and LM on A..

Logical reasoning Geometric proofs Euclidean/non-Euclidean geometries Formal/informal proofs Conditional statements Pythagorean Theorem Intersection of a plane with 3-d figures Congruence, similarity, triangle inequality theorem Properties of quadrilaterals, circles, parallel li..

Question: Prove mid-point theorem from converse of Basic Proportionality Theorem. [2 Mark] Answer: Given: D and E are the mid-points of AB and AC respectively of a triangle ABC. To prove: DE||BC Proof: .... (1) (Since D is the mid-point of AB, AD = DB) Fro..

Question: D, E and F are the mid-point of the sides BC, CA and AB respectively of a D ABC. Determine the ratio of the areas of D DEF and D ABC. [3 Mar /> Answer: By mid-point theorem DE||BC ....(1) AFDE is a parallelog..

With trigonometry we can find the height of a building or the width of a river without actually climbing or crossing. Certain basic definitions are necessary to further develop this subject. The ratios of two sides of a triangle are taken. There are six possible combinations. Each ra..

Question: If in a D ABC, DE||BC as shown in the figure. [3 Mark] Show that i. ii. Answer: If DE||BC (given) ... (1) (by basic proportionality theorem) Adding 1 on both sides,..

Let a body of mass m be placed on the surface of the Earth, whose mass is M and radius is R. From equation (4) Let the body be now placed at a height h above the Earth's surface. Let the acceleration due to gravity at that position be g | . For comparison, the ratio between g | and ..