In parallelogram ABCD, AB = x + 8, BC = 3x, and CD = 4x – 4. ABCD must be a

Question

I'm confused by this question. Please help me if you can. This are the answer choices.

(A) rectangle (B) rhombus (C) trapezoid (D) square (E) pentagon

We can lure out (E) as it is a parallelogram.

As AB=BC (x+8=3x) x=4; also if AB=CD (x+8=4x-4) x=4; and if BC=CD (3x=4x-4) x=4:

In conclusion, AB=BC=CD, so I'm left with the choices (B), (C) or (D), but I have to pick 1.

Answer 1

Hi Sona,

The answer AB = BC = CD = 12 is correct. This means all four sides are congruent, so the given parallelogram is a either square or a rhombus.

Without being told angle measures, this parallelogram fits the requirements of a rhombus. In order for this parallelogram to be a square, we'd also need to know that it has 4 right angles.

Answer B) RHOMBUS is correct. I hope this helps!

~Karen D.

https://www.dummies.com/education/math/geometry/properties-of-rhombuses-rectangles-and-squares/

Answer 2

As you said, you have 3 congruent (equal length) sides. So let's get as specific as we can with our remaining answers.

A trapezoid has at most, 2 congruent sides (sides of equal length), so that is out.

Rectangle: 2 pairs of congruent sides (so this is a possible answer)

Square: all 4 sides are qual length. (So this is a possible answer)

However, since not ALL rectangles have 3 or more congruent sides, and ALL squares have 4 congruent sides, the answer should be a square.

I hope that helps!!

Best,

Sam

Answer 3

Hi Sona,

In a parallelogram the opposite sides are congruent, so I set AB = CD and x = 4. I then plugged 4 into all the sides and they all equaled 12.

This is a square.

I hope this helps.