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Note: Figure not drawn to scale.
Triangles
ABC and
FED shown are congruent. Line segment
bar(XY) is parallel to
bar(AC), and the length of
bar(BY)=3. What is the length of
bar(XY) ?

| Note: Figure not drawn to scale. $\newline$ Triangles $A B C$ and $F E D$ shown are congruent. Line segment $\overline{X Y}$ is parallel to $\overline{A C}$ , and the length of $\overline{B Y}=3$ . What is the length of $\overline{X Y}$ ?

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Midpoint formula: find the midpoint

Full solution

Q. | Note: Figure not drawn to scale.

\newline

Triangles

A B C

and

F E D

shown are congruent. Line segment

\overline{X Y}

is parallel to

\overline{A C}

, and the length of

\overline{B Y}=3

. What is the length of

\overline{X Y}

?

Congruent triangles: Since triangles $ABC$ and $FED$ are congruent, corresponding sides are equal in length.
Corresponding sides equality: Therefore, $\overline{AC}$ is equal in length to $\overline{FE}$ .
Parallel lines and transversal: $\overline{XY}$ is parallel to $\overline{AC}$ , and since $\overline{BY}$ is a transversal, $\overline{BY}$ is also parallel to $\overline{XY}$ .
Length of BY given: The length of bar(BY) is given as $3$ .
Length of $XY$ determined: Since $\overline{BY}$ is parallel to $\overline{XY}$ and triangles $ABC$ and $FED$ are congruent, $\overline{XY}$ must be equal in length to $\overline{BY}$ .
Length of $XY$ determined: Since $\overline{BY}$ is parallel to $\overline{XY}$ and triangles $ABC$ and $FED$ are congruent, $\overline{XY}$ must be equal in length to $\overline{BY}$ .Therefore, the length of $\overline{XY}$ is also $3$ .

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