Question

given the information marked on each figure below, select all classifications that must be true. note that each figure is drawn like a rectangle, but you should not rely on the way the figure is drawn in determining your answers. if necessary, you may learn what the markings on a figure indicate. three figures with checkboxes for quadrilateral, parallelogram, rectangle below each

Explanation:

First Figure (ABCD):

Step1: Identify Quadrilateral

A quadrilateral is a 4 - sided polygon. ABCD has 4 sides, so it is a quadrilateral.

Step2: Identify Parallelogram

In a quadrilateral, if the diagonals bisect each other (the markings show that the segments of the diagonals are equal, so diagonals bisect each other), then it is a parallelogram. So ABCD is a parallelogram.

Step3: Identify Rectangle

For a parallelogram to be a rectangle, we need to check if it has right angles. But from the diagonal markings alone, we can't confirm right angles. Wait, actually, in a parallelogram, if the diagonals are equal, it is a rectangle. Wait, the markings: the diagonals have segments with one, two, and two, one marks? Wait, maybe I misread. Wait, the first figure: the diagonals are marked with two segments equal (the cross - marks). Wait, in a parallelogram, if the diagonals are equal, it is a rectangle. But if the diagonals bisect each other (which they do here as per the markings), and if we assume the diagonals are equal? Wait, no, the markings: let's re - evaluate. The first figure: ABCD is a quadrilateral (4 sides), diagonals bisect each other (so parallelogram), and if the diagonals are equal (the markings: two segments on one diagonal and two on the other? Wait, maybe the diagonals are equal. Wait, actually, in a parallelogram, equal diagonals imply a rectangle. But maybe the first figure: quadrilateral (yes), parallelogram (yes, diagonals bisect each other), and rectangle? Wait, no, maybe I made a mistake. Wait, the problem says "select all classifications that must be true". Let's start over.

First figure (ABCD):

• Quadrilateral: Yes, 4 - sided.
• Parallelogram: Diagonals bisect each other (markings show that the segments of the diagonals are equal, so diagonals bisect each other), so it is a parallelogram.
• Rectangle: In a parallelogram, if diagonals are equal, it is a rectangle. But the markings: are the diagonals equal? The markings on the diagonals: one diagonal has two segments with one mark and one with two marks? Wait, no, maybe the diagonals are congruent. Wait, maybe the first figure: quadrilateral (must be true), parallelogram (must be true), rectangle? Wait, no, maybe not. Wait, the note says "do not rely on the way the figure is drawn". So from the markings: diagonals bisect each other (so parallelogram), 4 sides (quadrilateral). For rectangle, we need right angles. But we can't confirm right angles from diagonal bisecting. Wait, I think I messed up. Let's look at the second figure.

Second Figure (GHIJ):

Step1: Identify Quadrilateral

GHIJ has 4 sides, so it is a quadrilateral.

Step2: Identify Parallelogram

The sides: GH and IJ are marked equal, GI and HJ are marked equal? Wait, no, the markings: two sides (GH and IJ) have one mark, and the other two (GI and HJ) have one mark? Wait, no, the figure is a quadrilateral with two pairs of opposite sides equal (the markings: GH = IJ and GI = HJ), so it is a parallelogram (since in a quadrilateral, if both pairs of opposite sides are equal, it is a parallelogram).

Step3: Identify Rectangle

For a parallelogram to be a rectangle, we need right angles. But from the side markings (opposite sides equal), we can't confirm right angles. So it is a parallelogram and a quadrilateral, but not necessarily a rectangle.

Third Figure (VWXY):

Step1: Identify Quadrilateral

VWXY has 4 sides, so it is a quadrilateral.

Step2: Identify Parallelogram

We have three right angles (at X, V, W? Wait, X has a right - angle mark, V and W and Y have angle marks. If three angles of a quadrilateral…

Answer:

First Figure (ABCD):

• Quadrilateral: Checked
• Parallelogram: Checked
• Rectangle: Unchecked (Wait, maybe I was wrong earlier. Wait, in a parallelogram, if the diagonals are equal, it is a rectangle. Wait, the first figure's diagonals: the markings. If the diagonals are equal (the segments on the diagonals: maybe the diagonals are equal). Wait, maybe the first figure: diagonals bisect each other and are equal, so it is a rectangle. I think I made a mistake earlier. Let's re - consider the first figure's markings. The diagonals have segments with one, two, and two, one marks? Wait, maybe the diagonals are equal. So if a parallelogram has equal diagonals, it is a rectangle. So first figure: quadrilateral (yes), parallelogram (yes), rectangle (yes).

Second figure: GHIJ has opposite sides equal (so parallelogram) and 4 sides (quadrilateral), but no right angles, so not rectangle.

Third figure: VWXY has right angles, so quadrilateral, parallelogram, rectangle.

So the correct check - marks:

First figure (ABCD):

• Quadrilateral: $\boldsymbol{\text{Checked}}$
• Parallelogram: $\boldsymbol{\text{Checked}}$
• Rectangle: $\boldsymbol{\text{Checked}}$ (if diagonals are equal, which from markings, maybe the diagonals are equal as the segments are marked with equal - length marks)

Second figure (GHIJ):

• Quadrilateral: $\boldsymbol{\text{Checked}}$
• Parallelogram: $\boldsymbol{\text{Checked}}$
• Rectangle: $\boldsymbol{\text{Unchecked}}$

Third figure (VWXY):

• Quadrilateral: $\boldsymbol{\text{Checked}}$
• Parallelogram: $\boldsymbol{\text{Checked}}$
• Rectangle: $\boldsymbol{\text{Checked}}$

Final Answer (Check - marks):

First figure (ABCD):

• Quadrilateral: $\boldsymbol{\text{Checked}}$
• Parallelogram: $\boldsymbol{\text{Checked}}$
• Rectangle: $\boldsymbol{\text{Checked}}$

Second figure (GHIJ):

• Quadrilateral: $\boldsymbol{\text{Checked}}$
• Parallelogram: $\boldsymbol{\text{Checked}}$
• Rectangle: $\boldsymbol{\text{Unchecked}}$

Third figure (VWXY):

• Quadrilateral: $\boldsymbol{\text{Checked}}$
• Parallelogram: $\boldsymbol{\text{Checked}}$
• Rectangle: $\boldsymbol{\text{Checked}}$