Question

Which of the following statements is true and would show that the 4 points are the vertices if a parallelogram?

A. DA=AB=BC=CD=square root 17
B. AB=CD=square root13;DA=BC=square root 17
C. DB= square root 18;AC=square root 38
D. M__=M=__=3/2
AB. AD

Answer 1

The true statement that shows the given points are the vertices of a parallelogram is AB=CD=square root13;DA=BC=square root 17.

Step-by-step explanation:

In order for the given points to be the vertices of a parallelogram, the opposite sides should be equal in length. Let's analyze each statement:

A. DA=AB=BC=CD=square root 17: This statement implies that all four sides of the parallelogram are equal in length, which means it is a rhombus, not a parallelogram. Therefore, this statement is not true.

B. AB=CD=square root13;DA=BC=square root 17: This statement indicates that AB and CD have the same length, as well as DA and BC. This satisfies the condition for a parallelogram, where opposite sides are equal. Hence, this statement is true.

C. DB= square root 18;AC=square root 38: This statement does not provide any information about the lengths of the sides AB, BC, CD, and DA. Therefore, it does not prove that the points are the vertices of a parallelogram. Hence, this statement is not true.

D. M__=M=__=3/2 AB. AD: This statement mentions points M and AD, which are not given in the question. Therefore, it is not related to the vertices of the parallelogram. Hence, this statement is not true.

Based on the above analysis, the only true statement that shows the given points are the vertices of a parallelogram is B. AB=CD=square root13;DA=BC=square root 17.