Thus:

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An aeroplane leaves an airport and flies due north at a speed of km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of km per hour. Two poles of heights 6 m and 11m stand on a plane ground. If the distance between the feet of the poles is 12 m, find the distance between their tops. In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes.

Prove that Solution:. Prove that the sum of the squares of the diagonals of parallelogram is equal to the sum of the squares of its sides. In the given figure, two chords Ab and CD of a circle intersect each other at the point P when produced outside the circle. Nazima is fly fishing in a stream. The trip of her fishing rod is 1.

Assuming that her string from the trip of the rod to the fly is that, how much string does she have out see the figure? If she pills in the string at the rate of 5 cm per second, what will be the horizontal distance of the fly from her after 12 seconds?

Two figures having the same shape but not necessarily the same size are called similar figures Two figures having the same shape as well as same size are called congruent figures Note that all congruent figures are similar but the similar figures need not be congruent.

Two polygons of the same number of sides are similar if i their corresponding angles are equal and ii their corresponding sides are in the same ratio or proportion. Two triangles are similar if i their corresponding angles are equal and ii their corresponding sides are in the same ratio or proportion Note : If the corresponding angles of two triangles are equal, then they are known as equiangular triangles.

The ratio of any two corresponding sides in two equiangular triangles is always the same. Basic Proportionality Theorem If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then other two sides are divided in the same ratio.

Converse of BPT If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side,. Formulae Handbook for Class 10 Maths and Science. Solution: Ex 6. Solution: Triangles Class 10 Ex 6. Recall that your have proved it in class IX Solution: Ex 6. Recall that your have done it in class IX Solution: Ex 6. Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form : Solution: Ex 6.

Prove that: Solution: Ex 6. Areas of these triangles are in the ratio a 2 : 3 b 4 : 9 c 81 : 16 d 16 : 81 Triangles Class 10 Ex 6. CD Solution: Ex 6.

Prove that Solution: Ex 6. Similarity of Polygons Two polygons of the same number of sides are similar if i their corresponding angles are equal and ii their corresponding sides are in the same ratio or proportion Similarity of Triangles Two triangles are similar if i their corresponding angles are equal and ii their corresponding sides are in the same ratio or proportion Note : If the corresponding angles of two triangles are equal, then they are known as equiangular triangles.

Basic Proportionality Theorem BPT and its Converse Basic Proportionality Theorem If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then other two sides are divided in the same ratio.

RD Sharma Class 12 Solutions. Watch Youtube Videos. Concurrency: Concurrency is a special type of numerical that you will come across while solving the problems of the exercise of the triangle. These sums can carry a lot of marks if they come in the board examination and solving it with proper steps can fetch you marks. Triangle with the Parallel Line: There can be sums where a parallel line can intersect with the triangle and you will be asked to find the missing angle. These sums can help you to increase your knowledge regarding the mensuration and you can take up civil engineering in the higher studies.

Finding the Missing Angle: In Exercise 6. Here are some basic tips to solve the sums on the triangle easily:. Learn the basic properties of triangle. Go through the question several times and try to understand the question. Note down everything that is already given in the sum. Take the right approach to solve the sum as you have practised before. Make sure writing all the steps of the sum while you are solving it. Once you find the answer, you need to mark it properly on your paper.

As the Ex 6. The most important thing that you will need to practise is drawing the triangle diagrams given in the book and label them properly.

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