Question

In triangle ABC and DEF, ∠B = ∠E, ∠F = ∠C and AB = 3 DE. Then, the two triangles are
(a) neither congruent nor similar (b) congruent as well as similar
(c) congruent but not similar (d) similar but not congruent

Answer 1

Answer:

Both The triangles are congruent as well as similar.

Answer 2

Solution :-

In ∆ABC and ∆DEF we have,

→ ∠ABC = ∠DEF { given }

→ ∠ACB = ∠DFE { given }

So,

→ ∆ABC ~ ∆DEF { By AA similarity }

now,

→ AB = 3•DE

→ AB/DE = 3/1

then,

→ AB/DE = BC/EF = AC/DF = 3/1 { When two ∆'s are similar, their corresponding sides are in same ratio .}

Now, we know that,

• When two ∆'s are congruent , ratio of corresponding sides is equal to 1 . { Because in congruent ∆'s corresponding sides are of equal measure . }

therefore, we can conclude that, ∆ABC is not congruent to ∆DEF .

hence, the two triangles are Option (D) similar but not congruent .

Learn more :-

*जर △ ABC ~ △ DEF असून AB = 12 सेमी and DE = 14 सेमी. तर △ ABC आणि △ DEF यांच्या क्षेत्रफळाचे गुणोत्तर किती?.*

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*In triangle ABC, DE || AB. If CD = 3 cm, EC = 4 cm, BE = 6 cm, then DA is equal to …………….*

1️⃣ 7.5 cm

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In the figure , Line PQ || Side BC AP = 6 , PB = 8 , AQ = x and QC = 12 , then write the value of x.

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