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maksim [4K]
3 years ago
8

In the figure, and bisect each other. Complete the statements to prove that quadrilateral ABCD is a parallelogram.

Mathematics
1 answer:
Alisiya [41]3 years ago
5 0

Observe the figure below.

    Statement                                                                          Reason

1. AC and BD bisect each other                                             Given

2. AE = EC and BE = ED                                                         Definition of bisection

3. m \angle AEB = m \angle CED                       Vertical angle theorem

Vertical angle theorem states " When two lines intersect each other, the vertically opposite angles are always equal".

4. \Delta ABE \cong \Delta CDE                         SAS criterion for congruence

5. m \angle ACD = m \angle CAB           Corresponding angles of congruent triangles are congruent

6. AB \parallel CD                                 Converse of alternate interior angle theorem

7.  m \angle BEC = m \angle AED                   Vertical angle theorem

8.  \Delta BEC \cong \Delta DEA            SAS criterion for congruence

9.  BC \parallel AD                                 Converse of alternate interior angle theorem

As, \Delta BEC \cong \Delta DEA, so m \angle CBD = m \angle BDA as corresponding parts of corresponding triangles are equal. As these angles are alternate interior angles, so the lines BC and AD are parallel by  "Converse of alternate interior angle theorem".

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417.084

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9*6.5+12*9.757+14*17.25

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The lunch lady had 5 pound of lasagna. If she makes 1/4-pound servings using this amount of lasagna, how many servings can she m
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HELPP!!! 30 POINTS!!! WILL MARK BRAINLYIST!! Step 1: Written Response (30 points) Using complete sentences, compare the fat cont
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median a= 65 b= 75 c=68

This shows the median of each fat content of each restaurant showing that restaurant c is closer to that of 'restaurant a ' than a is to 'restaurant b' and near to 1/7 lower than that of restaurant b which shows they are all highly skewed with each other upon their graph.

The measures of spread start with 55 to 72 for 'restaurant a' where the upper and lower quartiles  are 70-60 showing a distribution 10-17 into the whisker plot.

Compared to restaurant b which shows a measure of spread start with 65 to 90 for 'restaurant b' where the upper and lower quartiles are 85 - 68 into the whisker plot and show a spread of 3 in the left exterior and 5 spread in the right exterior to the upper quartile. So in comparison to restaurant a that restaurant b has a greater spread in the interquartile range = 15  where restaurant a =10.

For the outer quartile the comparison to restaurant a is twice as small meaning restaurant a is greater by over double and shown as   53 <a < 60 which when showing both outer quartiles we can use the amounts being 7 and 70<a<72 = 2

and show closed dots on equality line number line separately showing a<-7  and a>2 for each outer exterior quartile. For restaurant b this shows opposite similar equalities 65<b< 68 = b>-3 and   82<b<89 = b>7

So the differences are smaller for b for left side by 4 and larger for b by 5 up on the right side.

We compare both to restaurant c and find c =   60<c<61 = c>-1 and 70<c<71 = c>1 so the differences are that the outer quartile for c through the other quartiles = -2> c < -6 . This shows how smaller c is compared to a and b outer quartiles). We can also prove that while the outer quartiles are much more smaller for c than a and b we cna prove that c actually has an inner quartile more similar to c and closer distribution of b as the median is more closer for a and c where b has a greater output for median as restaurant b has the higher fat content and greater distribution within the inner quartiles over all.

Summary findings Restaurant c outer quartile is moderately skewed as they show -1 -0.5  on the left side and 1-0.5 on the right side. Restaurant a has a closer median inner quartile to c and closer distribution of inner distribution of c. It's output outer quartile distribiution is a distribution that is higher than b but a smaller inner quartile compared to b, when this happens then the distribution spread shows less range and fewer products to account for.

So i think restaurant b has the higher fat content to its menu.

Where restaurant a must be the healthiest as it holds the lowest range and larger gap is such range for healthier food.ie) when compared to the others. 

Meanings of what we are asked.

In a box and whisker plot: the ends of the box are the upper and lower quartiles, so the box spans the interquartile range. the median is marked by a vertical line inside the box. the whiskers are the two lines outside the box that extend to the highest and lowest observations.

Skewness refers to distortion or asymmetry in a symmetrical bell curve, or normal distribution, in a set of data. If the curve is shifted to the left or to the right, it is said to be skewed. Skewness can be quantified as a representation of the extent to which a given distribution varies from a normal distribution.

As a general rule of thumb:

If skewness is less than -1 or greater than 1, the distribution is highly skewed.

If skewness is between -1 and -0.5 or between 0.5 and 1, the distribution is moderately skewed.

If skewness is between -0.5 and 0.5, the distribution is approximately symmetric.

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defon

Answer:

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Step-by-step explanation:

If you are trying to find the volume, you would use the formula:

\pi \: r ^{2} (h)

You would plug in the radius (r), which is 58, and then plug in the height, which is 73.

Make sure you remember to use 3.14 and not the pi key if you are using a calculator.

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