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
$16$
$4$ Cevap
C
$5$
D
$2.25$

Cevap

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

Adım Adım Çözüm

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.

Anahtar Kavram

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

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

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