A quadrilateral has vertices A(4,5),B(2,4),C(4,3) , and D(6,4) . Which statement about the quadrilateral is true

A. ABCD is a parallelogram with noncongruent adjacent sides.
B. ABCD is a trapezoid with only one pair of parallel sides
C. ABCD is a rectangle with noncongruent adjacent sides.
D. ABCD is a square.
E. ABCD is a rhombus with non-perpendicular adjacent sides.

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nehagarg1321 nehagarg1321 · Answer 1 · 2024-07-08T06:03:58-04:00

Answer:

To determine which statement about the quadrilateral is true, we need to analyze the given vertices: A(4,5), B(2,4), C(4,3), and D(6,4).

Calculate the slopes of each side to check for parallel sides:

Slope of AB = (5 - 4) / (4 - 2) = 1 / 2

Slope of BC = (4 - 3) / (2 - 4) = 1 / (-2) = -1 / 2

Slope of CD = (3 - 4) / (4 - 6) = (-1) / (-2) = 1 / 2

Slope of DA = (4 - 5) / (6 - 4) = (-1) / 2 = -1 / 2

Since AB and CD have the same slope (1/2), and BC and DA have the same slope (-1/2), ABCD is a trapezoid with only one pair of parallel sides.

Thus, the correct statement is:

**B. ABCD is a trapezoid with only one pair of parallel sides.