Congruence of Triangles By SSS Criteria
Congruence of Triangles by SSS Criteria
Theorem: Two triangles are congruence if the three sides of one triangle are equal to the corresponding three sides of the other triangle.
Given: Two such that AB = DE, BC = EF and AC = DF.
To Prove:
Construction: Draw a line segment EG on the other side of EF such that AB = EG and . Join GF and GD.
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Proof: In BC = EF [Given] AB = GE [By construction] and, So, by SAS criterion of congruence, we have
Now, AB = DE and AB = GE
Similarly, AC = DF and AC = GF In DE = GE ....(iii) In DF = GF [From (ii)]
From (iii) and (iv), we have
But, Thus, in AB = DE [Given] and, AC = DF [Given] So, by SAS criterion of congruence , we have
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Illustration: ABCD is a parallelogram , if the two diagonals are equal, find the measure of
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Solution: Since ABCD is a parallelogram. Therefore, AB = CD and AD = BC [ Thus, in AD = BC [As proved above] BD = AC [Given] and, AB = AB [common] So, by SSS criterion of congruence, we have Now,
transversal is Hence, the measure of |
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Two isosceles triangles ABC and DBC having the common base BC such that AB = AC and DB = DC. Then
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| Right Option : B | |||
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In the given figure, AD is the median then ∠BAD is | |||
| Right Option : D | |||
| View Explanation | |||
In the figure shown above, if AB = DE, AC = DF and BC = EF, then which two triangles are congruent?
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| Right Option : C | |||
| View Explanation | |||
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Barkha Arora
10thIn terms of methodology I want to say that institute provides expert guidence and results oriented monitering supplements by requsite study material along with regular tests which help the students to improve their education skills.The techniques of providing education helps the students to asses...
Aman Kumar Shrivastava
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Ayan Ghosh
8thAbhyas institute is one of the best coaching institute in the vicinity of Ambala Cantt area. The teachers of the institute are well experienced and very helpful in solving the problems of the students.The good thing of the institute is that it is providing extra classes for the students who are w...
Aman Kumar Shrivastava
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Cheshta
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