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Inequality in TriangleIn this section, we shall discuss inequality in triangle.Theorem 1 : If two sides of a triangle are unequal, the longer side has greater angle opposite to it. Given : A ΔABC in which AC > AB. Prove that : ∠ABC > ∠ACB Construction : Mark a point D on AC such that AB = AD. Join BD.
Converse of the above theorem is also true. Theorem : 2 In a triangle the greater angle has the longer side opposite to it. _________________________________________________________________ 1) In ΔABC, AC = 5cm, AB = 7 cm and BC = 3Cm. Write the angles in ascending order. 2)In ΔPQR, PQ = 8cm, PR = 3 cm and PQ= 6Cm. Write the angles in ascending order. 3) In ΔABC, AC is the longest side then which angle is the largest ? 4) In ΔPQR, QR is the shortes side then which angle is the smallest ? 5) In a right triangle MNO, right angled at N, which side is the longest side? 6) n ΔPQR, ∠P =40 ^{0} ,∠Q =80 ^{0} and ∠R =60 ^{0} . Write the sides in ascending order. Triangles • Introduction to Triangles • Types of Triangles on the basis of Sides • Types of Triangles on the basis of Angles • Angle Sum Property of Triangles • Exterior and Interior angles of Triangle • Triangle Inequality Property • Congruent Triangles • Postulates of Congruent Triangle • Inequality in Triangle
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