Alex wants to draw two triangles ABC and DEF- such that-AB - DEBC- EF-C - -FWe have AB - 5 cm- BC - 6 cm and -C - 60- Can you construct the two triangles and are the two triangles congruent- Give reasons for your answer-

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Standard VII

Mathematics

Construction of a Triangle with SSS Criterion

Alex wants to...

Question

Alex wants to draw two triangles ABC and DEF, such that:
AB = DE
BC= EF
$∠ C = ∠ F$
We have AB = 5 cm, BC = 6 cm and $∠ C = 60^{\circ}$ . Can you construct the two triangles and are the two triangles congruent? Give reasons for your answer.

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Solution

Yes, we can construct the two triangles, the two triangles are not congruent.

Here, the two triangles are not congruent because for congruency, the angles which are equal should have been the included angles, B and E.

If there are two triangles given with equal sides and an equal angle which is non-included angle, then the two triangles are not congruent.

However, if we are given a triangle with 2 sides and a non-included angle, we can construct a triangle with that information.

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Alex wants to draw two triangles ABC and DEF, such that: AB = DE BC= EF ∠C=∠F We have AB = 5 cm, BC = 6 cm and ∠C=60∘. Can you construct the two triangles and are the two triangles congruent? Give reasons for your answer.

Alex wants to draw two triangles ABC and DEF, such that:
AB = DE
BC= EF
$∠ C = ∠ F$
We have AB = 5 cm, BC = 6 cm and $∠ C = 60^{\circ}$ . Can you construct the two triangles and are the two triangles congruent? Give reasons for your answer.