Triangle ABC is similar to triangle DEF, where vertex A corresponds to vertex D, vertex B … — SAT

Triangle $ABC$ is similar to triangle $DEF$ , where vertex $A$ corresponds to vertex $D$ , vertex $B$ corresponds to vertex $E$ , and vertex $C$ corresponds to vertex $F$ . The length of side $AB$ is $6$ , the length of side $BC$ is $8$ , and the length of side $DE$ is $3$ . What is the length of side $EF$ ?

A
$16$
$4$ Answer
C
$5$
D
$2.25$

Answer

The correct answer is

4

The correct answer is

4

. Since triangle

ABC

is similar to triangle

DEF

, the ratio of their corresponding side lengths must be equal. We set up the proportion

\frac{AB}{DE} = \frac{BC}{EF}

. Substituting the given values gives

\frac{6}{3} = \frac{8}{EF}

, which simplifies to

2 = \frac{8}{EF}

. Solving for

EF

gives

EF = 4

Step-by-Step Solution

Identify corresponding sides of the two similar triangles.

Since triangle

ABC

is similar to triangle

DEF

, side

AB

corresponds to side

DE

and side

BC

corresponds to side

EF

The ordering of vertices in similarity statements determines corresponding parts.

Set up a proportion using the ratios of corresponding sides.

The proportion is

\frac{AB}{DE} = \frac{BC}{EF}

, which translates to

\frac{6}{3} = \frac{8}{EF}

Corresponding sides of similar triangles are proportional.

Solve for the unknown length

EF

2 = \frac{8}{EF}

, which gives

EF = \frac{8}{2} = 4

Isolate the variable by simplifying the ratio and solving the algebraic equation.

Key Concept

The ratio of corresponding side lengths in similar triangles is constant.

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