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2 years ago

The figure below shows a quadrilateral ABCD. Sides AB and DC are congruent and parallel:

Mathematics

1 answer:

kirza4 [7]2 years ago

4 0

The statement that best describes a flaw in the students' proof is;

Option D; Angle DBC and angle BDA form a pair of corresponding angles, not a pair of alternate interior angles, which are congruent.

From the given image, we can see that;

AB ≅ DC

Let us analyze each given option;

A) ∠DBC and ∠BDA are in the same triangle ΔBDC. Now, they can't be a pair of vertical angles because vertical angles are a pair of opposite angles formed when two lines intersect but this is not the case here.

They are also not alternate interior angles because alternate angles are formed when a transverse line intersects two coplanar lines and again that is not the case here.

B) In ΔABD and ΔBDC, we see that;

AB = DC. Also, by theorem of alternate interior angles, we can tell that;

∠ABD = ∠BDC

Similarly, ∠BDA = ∠DBC from alternate interior angles.

Thus, there is one corresponding side and two non-included angles which means the triangles are congruent by AAS Congruency postulate.

C) As seen in B above, this statement is correct because the triangles are congruent by AAS postulate.

D) Corresponding angles lie on the same side of the transversal. In this case, ∠BDA and ∠DBC lie on opposite sides and are even congruent by alternate interior angles.

Read more about congruency at; brainly.com/question/7727792

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Find the slope of the line whose equation is 7x-2y=4

borishaifa [10]

Answer:

$\huge\boxed{\text{Slope: } \frac{7}{2}}$

Step-by-step explanation:

In order to find the slope of this equation, we can convert it into slope-intercept form, where we can find the slope more easily.

Slope intercept form is usually in the form $y=mx+b$ , where m is the slope and b is the y-intercept.

Let's algebraically manipulate this problem so we solve for y.

$7x - 2y = 4$
$-2y = 4 - 7x$ (Subtract 7x from both sides)
$y = -2 + \frac{7}{2}x$ (Divide both sides by -2)
$y = \frac{7}{2}x-2$ (Rearrange the equation)

From here, we can now see our equation is $y = \frac{7}{2}x-2$ , in the form $y=mx+b$ . Since m is the slope, and $\frac{7}{2}$ is m, our slope is $\frac{7}{2}$ .

Hope this helped!

6 0

3 years ago

Read 2 more answers

Sam is making a case for his calculator. It is a rectangular prism that will be 5.5 inches long by 2 inch wide by 5 inches high.

White raven [17]

Answer:

97in³

Step-by-step explanation:

L = 5.5, W = 2, H = 5

2(h × W) + 2(h × L) + 2(W × L)

= 2(5*2) + 2(5*5.5) + 2(2*5.5)

= 2(10) + 2(27.5) + 2(11)

= 20 + 55 + 22

= 97in³

8 0

3 years ago

a farmer wants to fence in three sides of a rectangular field shown below with 960 feet of fencing. The other side of the rectan

Alika [10]

9514 1404 393

Answer:

240 ft by 480 ft

Step-by-step explanation:

Area is maximized when the long side is half the total length of the fence. That makes the short side (out from the river) be half the length of the long side.

The fenced field dimensions are 240 feet by 480 feet.

You can let x represent the length of the long side. Then the length of the short side is half the remaining fence: (960 -x)/2.

The total area is the product of these dimensions:

A = x(960 -x)/2

We note that this is the equation of a parabola with zeros at x=0 and x=960. The maximum will be found on the line of symmetry, halfway between the zeros. That is at x = (0 +960)/2 = 480.

The area is maximized for a long-side dimension of 480 feet. The short sides are 240 feet.