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Complete Exercises solutions and a brief description about triangles, similarity of triangles, theorems and the facts related to this chapter are given below.
It will help the students to enhance their knowledge about the chapter triangles and the mathematician involved. Similarity of geometric figures is an important concept of Euclidean geometry.
Similarity in a geometric transformation of one figure into the other figure such that the measure of all linear elements of one figure are in proportion to the corresponding linear elements of the other figure. Two triangles or any 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. All congruent figures are similar but the similar figures need not be congruent.
Area Theorem: The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Pythagoras Byjus Class 9 Maths Chapter 6 Kindle theorem: In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
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We will try to solve your difficulty as soon as possible. What is meant by Similarity or Similar Triangle? What is Area Theorem in Class 10? In this section of the Class 10 Maths Chapter 6, students are introduced to the concept of similar figures. Students are taught the basis of similarity in figures such as squares or equilateral triangles with the same lengths of the sides, circles with the same radii. As the students progress through this topic, they get to understand that similar figures can have the same shape but not necessarily the exact size.
The questions from this topic mostly ask students to prove similarity between figures by applying the theorems. Once the students are made familiar with the concept of similarity, they are then introduced to the criteria under which two or more triangles are deemed similar. A thorough understanding of this topic will allow students to form the base for solving complex problems in higher mathematics. This section outlines and explains the criteria for the similarity of triangles.
The basic criteria for two triangles to be called similar include: if their corresponding angles are equal and if the corresponding sides of the triangles are in the same ratio or proportion. Students will be able to visualise the theorems as they are illustrated with the help of proper examples.
Students can understand the formula and learn the process for finding the surface area of similar triangles in this section. Students have already learnt the theorem and its proof in Class 9. In this section, students will learn how to prove this theorem by employing the concept of similarity of triangles. 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 Ch 2 Maths Class 10 Year 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 Class 6 Maths Chapter 1 Question Answer Video 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.
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