It is believed that the Persians and the Chinese had been using it to find the square and cube root of numbers.A triangle is a 2-dimensional closed figure that has three sides and angles. Although it has been named after Blaise Pascal, there have been traces of the triangle, long before Blaise Pascal was born. Since the condition has two different arrangements, we separate it into two conditions: the two angles and included side condition and the two angles and the side opposite a given angle condition.Īnswer: The triangle was invented by Blaise Pascal in 1653. There are three types of a triangle based on the length of the sides: equilateral, isosceles, and scalene.Īnswer: The two angles and any side condition determines a unique triangle. A triangle’s type depends on the length of its sides and the size of its angles (corners). There are different names for the types of triangles. Question 3: How many types of triangles are there?Īnswer: Triangles are shapes with three sides. A triangle can be simultaneously right and isosceles, in which case it is known as an isosceles right triangle. Further, a triangle with two sides equal is called isosceles, and a triangle with all sides a different length is called scalene. So, Using the SAS congruence rule we come to the conclusion thatΔ PQS ≅ Δ PRTĪnswer: An equilateral triangle property is that it has equal sides. Since angles opposite to equal sides are equal sides ∠Q = ∠R Show that PS=PT.Īnswer : In Δ PQS and Δ PRT, PQ=PR. Question 1: The figure below shows a triangle PQR with PQ=PR, S and T are two points on QR such that QT=RS. We use the ASA congruence rule to prove the property. On measuring the sides and angles respectively we come to the conclusion that the sides opposite to equal angles are also equal. For this, we need to measure the sides of the triangle with scale and angles with a protractor. This property is the converse of the above property. The sides opposite to equal angles of a triangle are also equal So by the Side-Angle-Side (SAS) rule Δ YXW ≅ Δ ZXWĪs the corresponding angles of congruent triangles, ∠XYW = ∠XZWĭownload NCERT Solutions for Class 10 Mathematics 2. Let’s draw the triangle first, with a point W as the bisector of ∠X. In an isosceles triangle XYZ, two sides of the triangle are equal. Angles opposite to equal sides of an isosceles triangle are also equal The following properties of triangles shall make the concept more clear to you: 1. Basic Proportionality Theorem and Equal Intercept Theorem.Pythagoras Theorem and its Applications.This implies that in every isosceles triangle, the angles opposite to the equal sides are also equal. On measuring the angles we observe that ∠Q and ∠R are also equal. Now using a protractor, measure the angles as well. What do you observe in the figure? The two sides of the triangle are equal. The figure given above is of an isosceles triangle PQR. Let’s see the figure given below before studying further about properties of triangles. When we study the properties of a triangle we generally take into consideration the isosceles triangles, as this triangle is the mixture of equality and inequalities. Right Angled triangle: A triangle with one angle equal to 90° is called right-angled triangle.Isosceles triangles and scalene triangles come under this category of triangles. Obtuse Triangle: The obtuse angled triangle is the one with one obtuse angled side.The best example of this kind of triangle is the equilateral triangle. Acute Triangle: Triangles, where all sides are acute-angled to each other, are called acute triangles.Scalene triangle: In a scalene triangle, no sides and angles are equal to each other.ĭepending on angles, triangles are of following types:.Isosceles triangle: An isosceles triangle is the one with two sides equal and two equal angles.This type of triangle is also called an acute triangle as all its sides measure 60° in measurement. Equilateral Triangles: An equilateral triangle has all the sides and angles of equal measurement.Depending on the measurement of sides and angles triangles are of following types: Triangles are three-sided closed figures.
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