In this article you will find out the Theorem of Class 10 from the Chapter 6 Triangle. We hope that this will help you to gain extra marks in your examination.
Some Important Points about Triangle
A triangle is a three-sided polygon that is one of the basic shapes in geometry. It is defined by three points called vertices, and the line segments that connect them are called sides. Triangles are characterized by their side lengths, angles, and other properties.
Triangles are classified based on their side lengths and angles into different types, including:
- Equilateral Triangle: A triangle in which all three sides are of equal length. All angles in an equilateral triangle are also equal, measuring 60 degrees each.
- Isosceles Triangle: A triangle in which two sides are of equal length. The angles opposite to the equal sides are also equal.
- Scalene Triangle: A triangle in which all three sides have different lengths. The angles in a scalene triangle can also have different measures.
Triangles can also be classified based on their angles into:
- Acute Triangle: A triangle in which all three angles are less than 90 degrees.
- Right Triangle: A triangle that has one angle measuring exactly 90 degrees. The side opposite the right angle is called the hypotenuse, and the other two sides are called the legs.
- Obtuse Triangle: A triangle in which one angle is greater than 90 degrees.
Triangles have various properties, such as the Pythagorean theorem for right triangles, which relates the lengths of the sides, and different formulas for calculating their area based on side lengths and heights. Triangles are used in many areas of mathematics, science, and real-world applications, including engineering, architecture, and physics.
Triangle Theorems with Proof Class 10
Theorem 6.1 Basic proportionality theorem (BPT) : If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.
Theorem 6.2 Converse of basic proportionality theorem (BPT) : If line a divides any two side of a triangle in the same ratio, then the line is parallel to third side.
Theorem 6.3 If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion) and hence the two triangles are similar.
Theorem 6.4 If in two triangles, sides of one triangle are proportional to (i.e., the same ratio of) the sides of the other triangle, then their corresponding angles are equal and hence the two triangles are similar.
Theorem 6.5 If one angle of a triangle is equal to one angle of the other triangle and sides including these angles are proportional then the triangles are similar.
