Or A shape is said to be similar to other, if the ratio of their corresponding sides is equal and the corresponding angles are equal. Note: The ratio of any two mxths sides in two equiangular triangles is always the. The angles on the same side of a transversal line are known as the corresponding angles, if both lie either above the two lines or below the two lines.
The following pairs of angles are called pairs of alternate interior angles. The pairs of interior angles on same side of the transversal line are called pair of consecutive interior angles. The following pair of angles are called alternate exterior angles. The following pair of angles are called vertically opposite angles. Mid-point theorem. Angle bisector theorem. In two triangles, if sides ppdf one triangle are proportional to i.
If Ch 4 Maths Class 10 Pdf Qualifications one angle of a triangle is class 10 maths ch 6 pdf qualifications to one angle of the other class 10 maths ch 6 pdf qualifications and the sides including these angles are proportional, then the two triangles are similar.
Pythagoras theorem. Converse of Pythagoras theorem. Previous Post Next Post. Contact form. LinkList ul li ul'. Tabify by Templateify v1.
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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 : 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 Class 8 Maths Chapter 13 Question Answer Pdf 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.
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 theorem: In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Visit to Discussion Forum to share your knowledge. This platform is being maintained to discuss the doubts of all students with experts and teachers. For any inconvenience, please contact us for help. 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? State Pythagoras theorem?
Chapter 7 - Coordinate Geometry. Chapter 8 - Introduction to Trigonometry. Chapter 9 - Some Applications of Trigonometry. Chapter 10 - Circles.
Chapter 11 - Constructions. Chapter 12 - Areas Related to Circles. Chapter 13 Ch 8 Class 10 Maths Introduction To Pdf - Surface Areas and Volumes. Chapter 14 - Statistics. Chapter 15 - Probability. Students were already introduced to the concept of Triangles in Class 9 wherein they studied properties such as congruence of Triangles. The introduction part of the chapter basically acts as a window for the students so that they are able to get an insight as to what would they be learning new under the topic of Triangles.
In this section of the Class 10 Maths Chapter 6, students are introduced to the concept of similar figures.
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