Question

Plot the given points and draw quad$ABCD$ and its diagonals. Also RUN the program above, inputting the given coordinates for the vertices. Then tell which of the following statement are true for the quad$ABCD$ .

I. Quad $ABCD$is a parallelogram.

II. Both pairs of opposite sides are congruent.

III. All sides are congruent.

IV. The diagonals are congruent.

V. The diagonals are perpendicular.

VI. The sides from four right angles.

a.$A\left(2,2\right),B\left(2,-2\right)C\left(-2,-2\right),D\left(-2,2\right)$

b.$A\left(0,3\right),B\left(3,0\right)C\left(0,-3\right),D\left(-3,0\right)$

Short answer

a. The true statements are I, II, III, IV, V and VI.

b. The true statements are I, II, III, IV, V, and VI.

Step-by-step solution

Part a. Step 1- Draw the figure.

Consider the Coordinates of the vertices of the quadrilateral $A\left(2,2\right),B\left(2,-2\right),C\left(-2,-2\right),D\left(-2,2\right)$.

Plot the figure as follows:

Step 2- Step description.

Now, the Conclusion from the statements:

I. Quadrilateral is parallelogram. True.

From the graph, it is clear that the opposite sides are congruent and parallel.

II. Both pairs of opposite sides are congruent.True.

From the graph, it is clear that both pairs of opposite sides are congruent.

III. All sides are congruent.True.

From the graph, it is clear that all sides are congruent

Step 3- Step description.

IV. The diagonals are congruent. True.

From the graph, it is clear that both the diagonals are congruent.

V. The diagonals are perpendicular.True.

From the graph, it is clear that both the diagonals are perpendicular to each other.

VI. The sides form four right angles.True.

From the graph, it is clear that the sides form right angles.

Thus, the true statements are I, II, III, IV, V and VI.

Part b. Step 1- Draw the figure.

Consider the Coordinates of the vertices of the quadrilateral$A\left(0,3\right),B\left(3,0\right),C\left(0,-3\right),D\left(-3,0\right)$ .

Plot the figure as follows:

Step 2- Step description.

Now, the Conclusion from the statements:

I. Quadrilateral is parallelogram. True.

From the graph, it is clear that the opposite sides are congruent and parallel.

II. Both pairs of opposite sides are congruent.True.

From the graph, it is clear that both pairs of opposite sides are congruent.

III. All sides are congruent.True.

From the graph, it is clear that all sides are congruent.

Step 3- Step description.

IV. The diagonals are congruent. True.

From the graph, it is clear that both the diagonals are congruent.

V. The diagonals are perpendicular.true.

From the graph, it is clear that both the diagonals are perpendicular to each other.

VI. The sides form four right angles.True.

From the graph, it is clear that the sides form right angles.

Thus, the true statements are I, II, III, IV, V and VI.