Question

your turn

1. according to the properties of rectangles, label each rectangle with the appropriate tick marks.

properties of rectangles
if a quadrilateral is a rectangle, then
if a parallelogram is a rectangle, then

Explanation:

Identify properties of a rectangle

Using the Properties of Squares knowledge point
A rectangle is a quadrilateral with four right angles. By definition, all four angles \(\angle A\), \(\angle B\), \(\angle C\), and \(\angle D\) are right angles.

Identify properties of a rectangle as a parallelogram

Using the Properties of Squares knowledge point
A rectangle is also a parallelogram. Therefore, its diagonals are congruent, meaning \(\overline{AC} \cong \overline{BD}\).

Determine appropriate tick marks

Using the Geometric Tick Marks knowledge point
For the first statement ("If a quadrilateral is a rectangle, then..."), we label the four corners with right-angle symbols (\(\llcorner\)). For the second statement ("If a parallelogram is a rectangle, then..."), we draw the congruent diagonals \(\overline{AC}\) and \(\overline{BD}\) and label them with matching single tick marks to show they are equal in length.

Answer:

To label each rectangle according to its properties:

1. First Rectangle (If a quadrilateral is a rectangle, then...):

• Place a right-angle symbol (\(\llcorner\)) in each of the four interior corners: \(\angle A\), \(\angle B\), \(\angle C\), and \(\angle D\).

1. Second Rectangle (If a parallelogram is a rectangle, then...):

• Draw the two diagonals, \(\overline{AC}\) and \(\overline{BD}\).
• Place a single tick mark on each diagonal to indicate that the diagonals are congruent (\(\overline{AC} \cong \overline{BD}\)).