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Maths Theorems List and Important Class 10 Maths Theorems (With Proofs)

Chapter 6 - Triangles Exercise Ex. So, we had observed that two respective sides are in same proportion in both triangles and also angle included between them is respectively equal. Let AD and PS be the medians of these triangles. So, all equilateral triangles are similar to each.

So, ratio between areas of these triangles will be equal to the square of the ratio between sides of these triangles. Hence, c Solution 9 If, two triangles are similar to each other, ratio between areas of these triangles will be equal to the square of the ratio between sides of these triangles. Given that sides are in the ratio Given that sides are 7 cm, 24 cm, and 25 cm.

Squaring the lengths of these sides we get 49,and Therefore, given triangle is satisfying Pythagoras theorem. So, it is a right triangle. The longest side in a right angled triangle is the hypotenuse. Given that sides are 3 cm, 8 cm, and 6 cm. Squaring the lengths of these sides we may get 9, 64, and Clearly, sum of squares of lengths of two sides is not equal to square of length of third.

Therefore given triangle is not satisfying Pythagoras theorem. So, it is not a right triangle. Given that sides are 50 cm, 80 cm, and cm. Squaring the lengths of these sides we may get, and Given that sides are 13 cm, 12 cm, and 5 cm.

We know that altitude bisects the opposite. So, length of each altitude will be Solution 7. Let OB be the pole and AB be the wire. Let these distances are represented by OA and OB respectively. Now applying Pythagoras theorem. Let CD and AB be the poles of height 11 and 6 m. Solution 5 i. Since respective angles are same and respective sides are. AB - 2DC. Let AB be the height of tip of fishing rod from water surface. Let BC be the horizontal distance of fly from the tip of fishing rod.

Then, AC is the length of string. Thus, length of ch 6 maths class 10 theorems modern out ch 6 maths class 10 theorems modern 3 m.

Now, she pulls string at rate of 5 cm per second. Let after 12 second Fly be at point D. Open navigation menu. Close suggestions Search Search. User Settings. Skip carousel. Carousel Previous. Carousel Next.

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Download. Related titles. Carousel Previous Carousel Next. Jump to Page. Search inside document. Ch 6 maths class 10 theorems modern 2 i Two equilateral triangles with sides 1 cm ch 6 maths class 10 theorems modern 2 cm. Hence, d. So, it is not a right triangle iii. Therefore given triangle is satisfying Pythagoras theorem. Hence, c. Let us join DB. BD Solution 5 i.

MD iii. Oxford University Press Children and Schools. Paddy Cool. Sagar Pattnaik. Ramesh raj. Karn Kumar. Genieline Velarde Magalona. Butt Amna. Natasha Ann Maranon. Ias Aspirant Abhi. Kriztelle A. Raprap Payte Baraquiel. Sandeep Sharma.

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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 Ch 6 Maths Class 10 Theorems For Forum to share your knowledge.

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What is meant Ch 10 Maths Class 10 Theorems Ii by Similarity or Similar Triangle? What is Area Theorem in Class 10? State Pythagoras theorem? State Converse of Pythagoras theorem. To verify and use results given in the curriculum based on similarity theorems. There are so many other important theorems based on similar triangles like If in two triangles, sides of one triangle are proportional to i. Or if two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar.

Historical Facts! Pythagoras theorem is famous because of its wide range of applications. Thales of Miletus � BC, Greece was the first known philosopher and mathematician. He is credited with the first use of deductive reasoning in geometry. He discovered many propositions in geometry.

While Maths is a little tricky, it is not difficult. It just requires a thorough understanding of the concepts, regular practice and a good hold on important formulas to score high marks in the Maths subject. Students must grasp all the formulas and theorems included in chapters like Triangles, Polynomials, Coordinate Geometry, Trigonometry and Mensuration as these chapters carry high weightage for Maths Board Exam Here, the graph consists of two intersecting lines.

Here, the graph consists of parallel lines. Here, the graph consists of coincident lines. Similarity of Triangles:. Mean: The mean value of a variable is defined as the sum of all the values of the variable divided by the number of values. Median: The median of a set of data values is the middle value of the data set when it has been arranged in ascending order.

That is, from the smallest value to the highest value. Median is calculated as. Where n is the number of values in the data. If the number of values in the data set is even, then the median is the average of the two middle values.

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