Based on sides, triangles have been classified into three categories:
Triangles are also divided into three classes on the basis of measure of the interior angles:
Example.1 In ΔABC, AB = 9, BC = 10, AC = 12. Find the length of median through A.
 In the adjacent figure AD is the required median. Using
 Apollonius theorem in the triangle we have,
2AD^{2} + 2(5)^{2} = 81+ 144 .
2AD^{2}_{ }+ 50 = 225
Example.2 The sides of the triangle are 6 cm, 8 cm, and 10 cm. Find the area, Inradius and Circumradius of the triangle.
 s =
In an equilateral triangle, all the sides are equal and all the angles are equal.
(a) Altitude =
(b) Area =
(c) Inradius =
(d) Circumradius =
The Tests for Congruency:
(a) SAS Test: Two sides and the included angle of the first triangle are respectively equal to the two sides and included angle of the second triangle.
(b) SSS Test: Three sides of one triangle are respectively equal to the three sides of the other triangle.
(c) ASA Test: Two angles and one side of one triangle are respectively equal to the two angles and one side of the other triangle.
(d) RHS Test: The hypotenuse and one side of a rightangled triangle are respectively equal to the hypotenuse and one side of another rightangled triangle.
Test for Similarity of Triangles:
(a) AAA Similarity Test: Three angles of one triangle are respectively equal to the three corresponding angles of the other triangle.
(b) SAS Similarity Test: The ratio of two corresponding sides is equal and the angles containing the sides are equal.
(c) SSS Similarity Test: The ratio of all the three corresponding side of the two triangles are equal.
Important Result
207 videos156 docs192 tests

1. What is a triangle? 
2. What are the types of triangles? 
3. What are some properties of triangles? 
4. How do you find the area of a triangle? 
5. Can a triangle have more than one right angle? 
207 videos156 docs192 tests


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