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. $A\left(1,1\right),B\left(3,4\right)C\left(10,4\right),D\left(8,1\right)$

b. $A\left(0,-3\right),B\left(-4,-1\right)C\left(-2,1\right),D\left(2,-1\right)$

Short answer

a. The true statements are I, II, IV.

b. The true statements are I, II, IV.

Step-by-step solution

Step 1.  Draw the figure.

Consider theCoordinates of the vertices of the quadrilateral $A\left(1,1\right),B\left(3,4\right),C\left(10,4\right),D\left(8,1\right)$.

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.False.

From the graph, it is clear that pairs of opposite sides are congruent and not 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.False.

From the graph, it is clear that both the diagonals are not perpendicular to each other.

VI. The sides form four right angles.False.

From the graph, it is clear that the sides do not form right angles.

Thus, the true statements are I, II, and IV.

Step 1.  Draw the figure.

Consider theCoordinates of the vertices of the quadrilateral $A\left(0,-3\right),B\left(-4,-1\right),C\left(-2,1\right),D\left(2,-1\right)$.

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.False.

From the graph, it is clear that pairs of opposite sides are congruent and not 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.False.

From the graph, it is clear that both the diagonals are not perpendicular to each other.

VI. The sides form four right angles.False.

From the graph, it is clear that the sides do not form right angles.

Thus, the true statements are I, II, and IV.