geometry honors

Can you prove ABCD is a parallelogram based on the given information? Explain.
Given: x = 5, y = 4
Prove: ABCD is a parallelogram.

The image consists of a quadrilatera ABCD with their sides AB, BC, CD, DA as 3x + 12, 7y - 8, 6x - 3 and 5y respectively.

1. 👍
2. 👎
3. 👁
1. To be a ||gm , opposite sides must be equal
7y-8 = 5y and 6x-3 = 3x+12

7y - 8 = 5y
2y = 8
y = 4

6x-3 = 3x+12
3x = 15
x = 5

Since the given information about x and y match those solutions, yes, it is a parallogram

or

just sub in the given values into the 4 different expressions to see that indeed opposite sides are equal

1. 👍
2. 👎

Similar Questions

1. math

Given: ABCD is a parallelogram AM , BN − angle bisectors DM = 4 ft, MN = 3 ft Find: The perimeter of ABCD

2. Geometry

Quadrilateral ABCD is a parallelogram. If adjacent angles are congruent, which statement must be true? A. Quadrilateral ABCD is a square. B. Quadrilateral ABCD is a rhombus. C. Quadrilateral ABCD is a rectangle. D. Quadrilateral

3. Geometry

Based on the information in the diagram, can you prove that the figure is a parallelogram? Explain. a. Yes; opposite sides are congruent. b. Yes; opposite angles are congruent. c. No; you cannot prove that the quadrilateral is a

4. math

The vertices of a parallelogram are A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4). Which of the following must be true if parallelogram ABCD is proven to be a rectangle?

1. Geometry

justify the last two steps of the proof. Given: ABCD is a parallelogram. Prove: triangleABC = triangleCDA 1. ABDC is a parallelogram 1. given 2. AB = DC and BC =DC 2. opposite sides of a parallelogram are congruent 3. AC = CA 3. ?

2. geometry

Given: QRST is a parallelogram. Prove: QRST is a square. Complete the proof below by choosing the reason for line number 2 and line number 6. Reason Statement 1. QRST is a parallelogram. Given 2. QRST is a rectangle 3. is a right

3. Geometry

Can the following quadrilateral be proven to be a parallelogram based on the given​ information? No. It is not a parallelogram because the angles of the quadrilateral do not add up to 360 degrees360°. B. No. It is not a

4. Mathematics

Using a ruler and a pair of compasses only, construct a parallelogram ABCD in which/ab/=8cm, abc=135° and the diagonal/ac/=12cm. Without making any calculations, construct a rhombus cdpq equal in area to ABCD with p and q on AB

1. Geometry

Given: ABCD is a parallelogram;

2. Math Algebra

The vertices of a quadrilateral ABCD are A (0, 5), B(9, 2), C (7, –4), and D(–2, –1). Is ABCD a rectangle? Prove using mathematical evidence and then justify your answer.

3. maths

If the point A(1,-2), B(2,3), C(-3,2), and D(-4,-3) are vertices parallelogram ABCD, then taking AB as the base , find the height of this parallelogram

4. geometry

7. Verify that parallelogram ABCD with vertices A(–5, –1), B(–9, 6), C(–1, 5), and D(3, –2) is a rhombus by showing that it is a parallelogram with perpendicular diagonals.