All categories

3 years ago

Prove that kn=mp and knmp is a parallelogram

Mathematics

1 answer:

____ [38]3 years ago

3 0

Answer:

See the paragraph proof below.

Step-by-step explanation:

Quadrilateral JKLM is given as a parallelogram. By a theorem, opposite sides JK and LM are congruent (1). By the definition of parallelogram, opposite sides KJ and ML are parallel. By the theorem on alternate interior angles, angles KJL and MLJ are congruent (2). Segments JN and PL are given as congruent (3). Using the three statements of congruence labeled above (1), (2), and (3), we now prove that triangles JKN and LMP are congruent by SAS. Sides of the triangles KN and PM are congruent by CPCTC. Sides of quadrilateral KNMP are given as parallel. Therefore, quadrilateral KNMP is a parallelogram by the theorem: If two sides of a quadrilateral are both parallel and congruent, then the quadrilateral is a parallelogram.

You might be interested in

A rental car agency charges $240 per week plus 0.25 per miles to my car how many miles can you travel in one week for 432.50

nataly862011 [7]

432.5-240= 192.50

192.50/.25=770miles

3 0

3 years ago

You are designing a diamond-shaped kite. you know that AD = 44.8 cm, DC = 72 cm, and AC = 84.8 cm. You want to use a straight cr

iVinArrow [24]

Correct me if I'm wrong, but i believe the correct answer should be answer C) 76 cm.

6 0

3 years ago

Read 2 more answers

Suppose that the travel time from your home to your office is normallydistributed with mean 40 minutes and standard deviation 7

Alex73 [517]

Answer:

The latest time that you should leave home is 12:08 PM

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 40, \sigma = 7$

If you want tobe 95 percent certain that you will not be late for an office appointment at 1 P.M.,what is the latest time that you should leave home?

How many minutes is the 95th percentile of travel time?

it is X when Z has a pvalue of 0.95. So it is X when Z = 1.645. So

$Z = \frac{X - \mu}{\sigma}$

$1.645 = \frac{X - 40}{7}$

$X - 40 = 7*1.645$

$X = 51.6$

Rouding up, the 95th percentile for travel time is 52 minutes.

52 minutes before 1PM is 12:08 PM.

The latest time that you should leave home is 12:08 PM

7 0

4 years ago

Which is the equation of the line that passes through the points (-4, 8) and (1, 3)?

MArishka [77]

Answer:

Therefore the equation is y=-x+4 (correct optlon: C)

Step-by-step explanation:

In order to find the equation that passes through both points, we can use the slope-intercept form of the linear equation:

y=mx+b

Where m is the slope and b is the y-intercept.

Using the given points on this equation, we have:

(-4,8):

(-4,8):8=m*(-4)+b

(-4,8):8=m*(-4)+bb=8+4m

(-4,8):8=m*(-4)+bb=8+4m(1,3):

(-4,8):8=m*(-4)+bb=8+4m(1,3):3=m+b

(-4,8):8=m*(-4)+bb=8+4m(1,3):3=m+b3=m+8+4m

(-4,8):8=m*(-4)+bb=8+4m(1,3):3=m+b3=m+8+4m5m=3-8

(-4,8):8=m*(-4)+bb=8+4m(1,3):3=m+b3=m+8+4m5m=3-85m=-5

(-4,8):8=m*(-4)+bb=8+4m(1,3):3=m+b3=m+8+4m5m=3-85m=-5m=-1

(-4,8):8=m*(-4)+bb=8+4m(1,3):3=m+b3=m+8+4m5m=3-85m=-5m=-1b=8+4*(-1)=8-4=4

Therefore the equation is y=-x+4 (correct optlon: C)

5 0

3 years ago

Morgan is making a square quilt with an area of 49 square feet for her nephew. The quilt is made out of square pieces that have

julia-pushkina [17]

Answer:

196 patches

Step-by-step explanation:

We are told that the quilt is made out of square pieces that have a perimeter of 24 square inches.

This means that, length of one side = 24/4 = 6 inches.

Now since Morgan is making a square quilt with an area of 49 square feet for her nephew, let's convert 6 inches to ft.

6 inches = 6 × 1/12 = 0.5 ft

Thus, the area of a small quilt = 0.5 × 0.5 = 0.25 ft²

Number of patches = 49/0.25 = 196 patches

3 0

3 years ago

Prove that kn=mp and knmp is a parallelogram ​

Prove that kn=mp and knmp is a parallelogram