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2 years ago

The following is an incomplete paragraph proving that the opposite sides of parallelogram ABCD are congruent:

Mathematics

2 answers:

OverLord2011 [107]2 years ago

8 0

<span>D) Angles BAC and DCA are congruent by the Alternate Interior Angles Theorem.</span>

Anestetic [448]2 years ago

5 0

Answer:

D. Angles BAC and DCA are congruent by the Alternate interior angles theorem.

Step-by-step explanation:

Given ABCD is a parallelogram.

AB=CD and BC=AD

$AB\parallel CD \; and\; BC\parallel AD$

To prove that $AB\cong CD\; and\; BC\cong AD$ .

Proof: According to given information

$AB\parallel CD$ and segment $BC\parallel AD$ .

Construct diagonal AC with a straightedge.

In $\triangle ABC\; and\; \triangle ADC$

AC=AC

Reflexive property of equality.

$m\angle BCA\cong m\angle DAC$

By alternate interior angles theorem.

$m\angle BAC\cong m\angle DCA$

By alternate interior angles theorem.

$\triangle BCA\cong\triangle DAC$

By ASA( Angle-Side_Angle) theorem.

By CPCTC opposite sides AB and CD, as well as BC and DA are congruent.

Hence proved.

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3 years ago

Which is bigger? four liters or one gallon?

hjlf

4 liters is slightly bigger

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2 years ago

Segment addition with variables

oksian1 [2.3K]

<em>x equals 22</em>

<h2>Explanation:</h2>

____________________________________________

The Segment Postulate states the following:

<em>Given two end points A and B, a third point C lines on the segment AB if and only if the distances between the points satisfy the equation:</em>

$\overline{AB}=\overline{AC}+\overline{CB}$

____________________________________________

From the figure:

$\overline{AC}=8+x \\ \\ \overline{CB}=10 \\ \\ \overline{AB}=40$

Our goal is to find x:

$\overline{AB}=\overline{AC}+\overline{CB} \\ \\ Substituting \ values: \\ \\ 40=(8+x)+10 \\ \\ 18+x=40 \\ \\ Subtracting \ 18 \ from \ both \ sides: \\ \\ 18-18+x=40-18 \\ \\ \boxed{x=22}$

<h2>Learn more:</h2>

Dilation: brainly.com/question/2501119

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2 years ago

Point D is located on MN at (2,43). What ratio relates MD to DN?

Eva8 [605]

The ratio of MD to DN is equal to 2.

<h3>How to find the partition ratio for a line segment</h3>

In accordance with the image set aside, the locations of the points M and N are M(x, y) = (- 6, - 4) and N(x, y) = (6, 4), respectively. Now we determine the vectors associated to line segments MD and DN by vector sum:

<u>MD</u> = D(x, y) - M(x, y)

<u>MD</u> = (2, 4 / 3) - (- 6, - 4)

<u>MD</u> = (8, 16 / 3)

<u>DN</u> = N(x, y) - D(x, y)

<u>DN</u> = (6, 4) - (2, 4 / 3)

<u>DN</u> = (4, 8 / 3)

Lastly, we find the length of each line segment by Pythagorean theorem:

MD = √[8² + (16 / 3)²]

MD = (8 / 3)√13

DN = √[4² + (8 / 3)²]

DN = (4 / 3)√13

And the ratio of MD to DN is:

MD / DN = [(8 / 3)√13] / [(4 / 3)√13]

MD / DN = 2

The ratio of MD to DN is equal to 2.

<h3>Remark</h3>

The statement presents typing mistakes, we kindly present the correct form below:

<em>Point D is located on line segment MN at (2, 4 / 3). What ratio relates MD to DN?</em>

To learn more on line ratios: brainly.com/question/3148758

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1 year ago

Item 18 you and your friend are selling tickets to a charity event. you sell 7 adult tickets and 16 student tickets for $120. yo

quester [9]

Answer:

Step-by-step explanation:

The two purchases can be written in terms of the cost of an adult ticket (a) and the cost of a student ticket (s):

7a +16s = 120 . . . . . . . . price for the first purchase

13a +9s = 140 . . . . . . . . price for the second purchase

Using Cramer's rule, the value of s can be found as ...

s = (120·13 -140·7)/(16·13 -9·7) = 580/145 = 4

The cost of a student ticket is $4.

_____

<em>Comment on Cramer's Rule</em>

Cramer's rule is particularly useful for systems that don't have "nice" numbers that would make substitution or elimination easy methods to use. If you locate the numbers in the equation, you can see the X-patterns that are used to compute the numerator and denominator differences.

The value of a is (16·140 -9·120)/(same denominator) = 1160/145 = 8. I wanted to show you these numbers so you could see the numerator X-pattern for the first variable.

Of course, graphical methods can be quick and easy, too.

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3 years ago