# Inequality in Triangle

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**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.

Statements |
Reasons |

1) AB = AD | 1) By Construction |

2) ∠ ABD = ∠ADB | 2) If two sides are equal then angle opposite to them are also equal |

3)∠ADB > ∠DCB | 3)As ∠ADB is an exterior angle of ΔBCD and exterior angle is always greater than interior angle. |

4)∠ADB > ∠ACB | 4)∠ACB = ∠DCB |

5) ∠ABD > ∠ABC | 5) ∠ABC = ∠ABD + ∠DBC |

6) ∠ABC > ∠ACB | 6) From (4) and (5) |

**Converse of the above theorem is also true.**

**Theorem : 2 In a triangle the greater angle has the longer side opposite to it.**

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**Practice**

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

• 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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