Theorem: The sum of any two side of a triangle is greater than the third side.
Given: To Prove: Construction: Produce side BA to D such that AD = AC. Join CD. Proof: In we have AC = AD [By construction] [Angles opp. to equal sides are equal] [] [] [ Side opp. to greater angle is larger] [ (By construction)] Thus, Similarly, |
Illustration: Prove that any two sides of a triangle are together greater than twice the median drawn to the third side.
Given: in which AD is a median. To Prove: Construction: Produce AD to E such that AD = DE. Join EC. Proof: In and EDC, we have AD = DE [By construction] BD = DC [ D is the mid point of BC] and, [ver. opp. are equal ] So, by SAS criterion of congruence , we have
[Corresponding parts of congruent triangles are equal right] Thus, in we have [ Sum of any two sides of a is greater than the third] [ AD = DE AE = AD +DE = 2AD and EC = AB] |
In S is any point on the side QR. Then Which of the following is true in case of ? | |||
Right Option : A | |||
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Of the following which option represents the sides of a triangle? | |||
Right Option : A | |||
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Two sides of a triangle are of lengths 8 cm and 2.5 cm.The lengths of third side can not be _________________ . | |||
Right Option : C | |||
View Explanation |
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