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3 years ago

Corresponding angles of ΔABC and ΔDEF are congruent. Does this prove that the triangles are congruent? Justify.

Mathematics

2 answers:

Varvara68 [4.7K]3 years ago

5 0

Answer:

The correct option is C.

Step-by-step explanation:

The required answer is "no".

It is given that corresponding angles of ΔABC and ΔDEF are congruent. It means

$\angle A\cong \angle D$

$\angle B\cong \angle E$

$\angle C\cong \angle F$

From this information we can say that by AAA property of similarity

ΔABC $\sim$ ΔDEF

The lengths of the sides of the two triangles are not necessarily equal.

Since the property AAA only guarantees similarity, therefore the corresponding angles of ΔABC and ΔDEF are congruent does not prove that the triangles are congruent.

The properties of congruent triangle are : SSS, SAS, ASA, AAS.

It means at least one side is required to say that the triangles are congruent.

Option C is correct.

Vsevolod [243]3 years ago

4 0

NO. Three congruent angles only proves the triangles are similar. You must have at least one side length to prove congruency.

SSS, SAS, ASA, AAS prove triangle congruency.

Answer: C

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Answer and explanation:

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Hope this helps!

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3 years ago

Read 2 more answers

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Answer:

Just plus everything together

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Step-by-step explanation:

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3 years ago

A particular airport has beacons on the ground 6 km out from the start of each runway. An airplane is directly over this beacon

hodyreva [135]

Answer:

6.06 km

Step-by-step explanation:

The information given in the question can be represented by the three sides if a right angled triangle.

Let the direct line from the airplane to the start of the runway be represented by x. So that applying the appropriate trigonometric function, we have;

Cos θ = $\frac{adjacent}{hypotenuse}$

Cos $8^{o}$ = $\frac{6}{x}$

0.9903 = $\frac{6}{x}$

⇒ x = $\frac{6}{0.9903}$

= 6.0588

x = 6.06 km

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