Question

Give the most precise name for the polygon formed by points A, B, C, and D.

Answer 1

Step 1. The figure formed by the points A, B, C, and D is shown in red in the following image:

We need to determine the most precise name for this figure.

Step 2. The options we are given are:

-Trapezoid

-Isosceles triangle

-Rhombus

-Parallelogram

A diagram of these 4 figures:

The figure is not a trapezoid, and it is also not an isosceles triangle.

Step 3. To distinguish between the rhombus and the parallelogram we consider the following property of these figures:

In a rhombus all of the sides are equal, and in a parallelogram, sides can be different but opposite sides are equal.

Therefore, we need to determine the length of the sides of our figure.

Step 4. The top side and the bottom side have a length of 5:

To find the length of the diagonal side, we use the Pythagorean theorem:

Therefore, the length of the diagonal sides is:

`\begin{gathered} √(3^2+4^2) \\ \downarrow \\ √(9+16) \\ \downarrow \\ √(25) \\ \downarrow \\ 5 \end{gathered}`

The diagonal sides are also 5,

Therefore, since all of the sides are equal, the figure is a rhombus.

Answer:

C. rhombus