Question

Triangle ABC ~ triangle DEF. Use the image to answer the question.

a triangle ABC with side AB labeled 11, side CA labeled 7.6 and side BC labeled 7.9 and a second triangle DEF with side DE labeled 3.3

Determine the measurement of EF.

EF = 1.1
EF = 1.39
EF = 2.37
EF = 3.3

Answer 1

The answer is EF = 2.37

We can use the AA Similarity Theorem to prove that triangle ABC is similar to triangle DEF. The AA Similarity Theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.

In triangle ABC, angle A is congruent to angle D because they are both vertical angles. Angle B is congruent to angle E because they are both corresponding angles. Therefore, triangle ABC is similar to triangle DEF by the AA Similarity Theorem.

Since the two triangles are similar, the sides of the triangles are in proportion. We can write this proportion as: \dfrac{AB}{DE} = \dfrac{BC}{EF} = \dfrac{CA}{DF}

We are given that AB = 11, DE = 3.3, and CA = 7.6. We can solve for EF using the following equation:

\dfrac{EF}{3.3} = \dfrac{11}{7.6}

EF = \dfrac{11}{7.6} \times 3.3

EF = 2.37

Explanation:

Answer 2

Answer:

We can use the property of similar triangles to solve this problem. The triangles formed by the given sides are similar. Let's call the length of EF "x". Then we can set up the following proportion:

AB/DE = BC/EF

Plugging in the given values, we get:

11/3.3 = 7.9/x

Cross-multiplying, we get:

11x = 7.9 * 3.3

Simplifying, we get:

11x = 26.07

Dividing both sides by 11, we get:

x = 2.37

Therefore, the measurement of EF is 2.37. Answer: (C) EF = 2.37.

Explanation: