Chapter-6 Triangles
Chapter-6 Triangles Triangle is a polygon which has three sides and three vertices. Triangles having same shape and size are said to be congruent. The similarity of triangles uses the concept of similar shape and finds great applications. Triangles are said to be similar if: a. Their corresponding angles are equal. b. Their corresponding sides are in the same ratio. Theorems and Proofs Theorem: If a line divides any two sides of a triangle in the same ratio, then the line is said to be parallel to the third side. Let ABC be a triangle with sides AB, AC and BC. DE divides any two sides of the triangle in the same ratio. Given : Line divides a triangle in the same ratio. Thus, A D D B = A E E C Proof: A D D B = A E E C (Given)—-(1) Let us assume that DE is not parallel to BC. Now we draw DE’ which is assumed to be parallel to BC. So, A D D B = A E ′ E ′ C (Property of similar triangles)—-(2) Therefore, from (1) and (2...