Questions: What type of figure is formed by joining the midpoints of a rectangle (see the figure to the right)? Justify your answer. Choose the correct answer below. A. The figure is a trapezoid. By SSS, triangle ECF is congruent to triangle GBF is congruent to triangle EDH is congruent to triangle GAH. B. The figure is a rectangle. By SSS, triangle GBF is congruent to triangle GAH. C. The figure is a rhombus. By SAS, triangle ECF is congruent to triangle GBF is congruent to triangle EDH is congruent to triangle GAH. D. The figure is a square. By SAS, triangle ECF is congruent to triangle EDH.

What type of figure is formed by joining the midpoints of a rectangle (see the figure to the right)? Justify your answer.

Choose the correct answer below.
A. The figure is a trapezoid. By SSS, triangle ECF is congruent to triangle GBF is congruent to triangle EDH is congruent to triangle GAH.
B. The figure is a rectangle. By SSS, triangle GBF is congruent to triangle GAH.
C. The figure is a rhombus. By SAS, triangle ECF is congruent to triangle GBF is congruent to triangle EDH is congruent to triangle GAH.
D. The figure is a square. By SAS, triangle ECF is congruent to triangle EDH.

Transcript text: What type of figure is formed by joining the midpoints of a rectangle (see the figure to the right)? Justify your answer. Choose the correct answer below. A. The figure is a trapezoid. By SSS, $\triangle E C F \cong \triangle G B F \cong \triangle E D H \cong \Delta G A H$. B. The figure is a rectangle. By SSS, $\triangle G B F \cong \triangle G A H$. C. The figure is a rhombus. By SAS, $\triangle E C F \cong \triangle G B F \cong \triangle E D H \cong \triangle G A H$. D. The figure is a square. By SAS, $\triangle E C F \cong \triangle E D H$.

Solution

Solution Steps

Step 1: Identify the Midpoints

The figure is formed by joining the midpoints of a rectangle. Let's denote the midpoints of the sides of the rectangle $ABCD$ as $E, F, G,$ and $H$.

Step 2: Analyze the Properties of the Midpoints

Since $E, F, G,$ and $H$ are midpoints, each segment connecting these points is parallel to the sides of the rectangle and half the length of the sides of the rectangle.

Step 3: Determine the Shape Formed

By joining the midpoints of a rectangle, the resulting figure is a rhombus. This is because:

All sides of the figure $EFGH$ are equal in length (each being half the length of the rectangle's sides).
The opposite angles are equal, and the diagonals bisect each other at right angles.