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Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians. Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals. Areas of these triangles are in the ratio a 2 : 3 b 4 : 9 c 81 : 16 d 16 : Sides of triangles are given below.
Determine which of them are right triangles. In case of a right triangle, write the length of its hypotenuse. CD Solution:. ABC is an isosceles triangle right angled at C. ABC is an equilateral triangle of side la.
Find each of its altitudes. Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals. A ladder 10 m long reaches a window 8 m above the ground. A guy wire attached to a vertical pole of height 18 m is 24 m long and has a stake attached to the other end.
How far from the base of the pole should the stake be driven so that the wire will be taut? 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.
This is done using concepts of common angle, alternate angle, and corresponding angles of similar triangles rules. This question is similar to question 12 where the sides of two triangles and their median Class 10 Maths Ch 7 Ex 7.1 Filetype Pdf are proportional, and you need to prove that the two triangles are similar. This question is solved by extending the median of both the triangles by equal length and then using rules of a parallelogram, SSS, SAS, Ncert Class 10 Maths Ch 6 Ex 6.3 Guide and corresponding angles of similar triangles criterion to prove that the triangles are similar.
This is a question on a vertical pole and its shadow along with the shadow of a tower. Two similar triangles are given, and students need to prove that the ratio of sides of the triangles and their medians are equal. Using the property of the median and corresponding angle similarity criterion, one can solve this problem.
All the problems in the Ex 6. The solutions are available in downloadable PDF format, which can also be printed out for a quick revision. The expert team of Vedantu has based all the answers on the CBSE curriculum; hence you can expect to score high marks in maths. 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.
Once you are able to draw the triangle diagram correctly, it will be easier for you to derive the answer.
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