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Give two different examples of pairs of i similar figures. State whether the following quadrilaterals are similar or not.
In the given figure i and ii , DE BC. Find EC in i and AD in ii. Show that EF QR. Show that BC QR. Using B. Recall that your have proved it in class IX Solution:.
Using converse of B. Recall that your have done it in class IX Solution:. State which pairs of triangles in the given figures are similar. Write the similarity criterion used by you for answering the question and also write the pairs of Ncert Solutions For Class 10 Maths Ch 6 Ex 6.3 Github similar triangles in the symbolic form :.
Prove that: Solution:. A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long.
Find the height of the tower. If the areas of two similar triangles are equal, prove that they are congruent. 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. You also need to give the correct notation for describing similar triangles. In the second question of Class 10 Maths Chapter 6 Exercise 6.
You need to apply the theorem for alternate interior angles and vertically opposite angles to solve this problem. In this question, a triangle is given, which contains two triangles inside of it. By applying the theorem that if the sides of a triangle are proportional, then their corresponding angles are equal, you can prove that the two interior triangles are similar. This is a straightforward question where two angles of two triangles are the same AA criterion hence students can prove that the given triangles are similar.
This question of Class 10 Maths Exercise 6. In this question of Triangles Class, 10 Exercise 6. You will be using the concept of vertically opposite angles and common angles to solve this question. This is again a simple question where two right triangles are given which have a common side, and you need to prove that both are similar triangles which can be easily proved with a common angle, corresponding sides of similar triangles, and alternate angle concept.
Class 10 Maths Exercise 6. In this problem, an isosceles triangle is given, and one of its sides is extended, and a perpendicular is dropped from the extended point to the opposite side of the triangle.
Students need to prove that the triangle formed by extension and the triangle formed by dropping a perpendicular to the base of the original triangle are similar. The properties of the isosceles triangle and alternate angle criterion are used to solve this problem.
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