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Triangles ABC and FDE are shown. The length of side AB is 15 inches. The length of side FD is 11 inches. Sides BC and DE are congruent. Sides AC and FE are congruent. Given AC ≅ FE and CB ≅ ED, which statement is correct?

1) Angle A is larger than angle B.
2) Angle C is congruent to angle E.
3) Angle C is smaller than angle E.
4) Angle C is larger than angle E.

2 Answers

4 votes

Answer:

D

Step-by-step explanation:

Angle C is larger than angle E.

User Banesto
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3 votes

Final answer:

Based on the triangle inequality principle, where the larger side is opposite the larger angle, angle C of triangle ABC is larger than angle E of triangle FDE because side AB is longer than side FD.

Step-by-step explanation:

To determine which statement is correct regarding triangles ABC and FDE, we must use the information given about congruent sides and apply the properties of triangles. Because sides AB and FD are not congruent (15 inches and 11 inches respectively), triangles ABC and FDE are not congruent. However, since it is given that AC ≡ FE and CB ≡ ED, these triangles are at least isosceles, with two sides of equal length.

We have to delve into the triangle inequality principle, which says the larger the side, the larger the angle opposite it. Since side AB is longer than side FD, angle C in triangle ABC must be larger than angle E in triangle FDE, as they oppose these sides respectively. Therefore, the correct answer is that angle C is larger than angle E. We apply this principle to determine the relation between angles C and E.

So, according to the information given and using the triangle inequality principle, the correct statement from the options provided is:
4) Angle C is larger than angle E.

User Tinstaafl
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