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Exercise 6. You can also download Maths Class 10 to help you to revise complete syllabus and score more marks ncert solutions for class 10 maths ch 6 ex 6.6 mac your examinations. Fill in the blanks by using the correct word given in brackets.

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 iiDE 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 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 : ncert solutions for class 10 maths ch 6 ex 6.6 mac b 4 : 9 c 81 : 16 d 16 : Sides of triangles are given.

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 ncert solutions for class 10 maths ch 6 ex 6.6 mac 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 ncert solutions for class 10 maths ch 6 ex 6.6 mac 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.

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 Ncert solutions for class 10 maths ch 6 ex 6.6 mac 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 ncert solutions for class 10 maths ch 6 ex 6.6 mac 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.

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NCERT Solutions for Class 10 Maths Chapter 6 Triangles are provided here which is considered to be one of the most important study material for the students studying in CBSE Class Chapter 6 of NCERT Solutions for Class 10 Maths is the triangles and it covers a vast topic including a number of rules and theorems. Students often tend to get confused which theorem to use while solving one. Solution: Ex Class 10 Maths Question 4. In the given figure, ABC is atriangle in which ?ABC 90� and AD ? CB. Prove that AC 2 = AB 2 + BC 2 � 2BC X BD Solution: Ex Class 10 Maths Question 5. In the given figure, Ad is a median of a triangle ABC and AM ? BC. Prove that Solution: Ex Class 10 Maths Question 6.

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