1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Naily [24]
3 years ago
6

Prove that the segments joining the midpoint of consecutive sides of an isosceles trapezoid form a rhombus.

Mathematics
1 answer:
Stella [2.4K]3 years ago
7 0

Answer:

B. See explanation

Step-by-step explanation:

Use the distance formula between two points (x_1,y_1) and (x_2,y_2):

d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}

Find the lengths of all sides of quadrilateral DEFG:

DE=\sqrt{(-a-b-0)^2+(c-2c)^2}=\sqrt{(a+b)^2+c^2}\\ \\EF=\sqrt{(a+-b-0)^2+(c-2c)^2}=\sqrt{(a+b)^2+c^2}\\ \\FG=\sqrt{(a+b-0)^2+(c-0)^2}=\sqrt{(a+b)^2+c^2}\\ \\GD=\sqrt{(-a-b-0)^2+(c-0)^2}=\sqrt{(a+b)^2+c^2}\\ \\

All sides are of the same length. Now fond the slopes of all sides:

DE=\dfrac{2c-c}{0-(-a-b)}=\dfrac{c}{a+b}\\ \\EF=\dfrac{c-2c}{a+b-0}=-\dfrac{c}{a+b}\\ \\FG=\dfrac{c-0}{a+b-0}=\dfrac{c}{a+b}\\ \\GD=\dfrac{c-c}{-a-b-0}=-\dfrac{c}{a+b}\\ \\

The slopes of the sides DE and FG are the same, so these sides are parallel. The slopes of the sides EF and GD are the same, so these sides are parallel.

You might be interested in
Find X when y= -2 <br> Thank you for your help and have a blessed day
Andreas93 [3]

Answer:

x = -5

Step-by-step explanation:

4x+y=2(x+3y)\\\\4x-2=2(x+3(-2))\\\\4x-2=2(x-6)\\\\4x-2=2x-12\\\\4x-2+2=2x-12+2\\\\4x=2x-10\\\\4x-2x=2x-2x-10\\\\2x=-10\\\\\frac{2x=-10}{2}\\\\\boxed{x=-5}

Hope this helps.

8 0
3 years ago
Read 2 more answers
The sides of a cube are numbered 4, 5, 6, 7, 8, and 9. What is the probability of rolling a 6?
Fiesta28 [93]

Answer:

1/6

Step-by-step explanation:

out of 6 numbers in total there is only one 6 therefore there is only 1/6 chances

7 0
3 years ago
Read 2 more answers
Please help if u can! :)))
jasenka [17]
Should be 11.53256.
6 0
3 years ago
What does quantitative data mean?
Serhud [2]
Quantitative data<span> is information about quantities; this is the only way I know how to explain,information that can be measured and written down with numbers is known as quantitative data! Heres an example,youre height!
: D</span>
4 0
3 years ago
Instead of dividing 400 by 16, Chip thought of an equivalent division problem that was easier for him to divide. Write an equiva
galben [10]
You can divided each by 4 and get this easy answer..

100 divided by 4= 25. Hope it helps!
5 0
3 years ago
Other questions:
  • For 50 points please help
    15·1 answer
  • Donna makes $9.75 per hour at her job. Kaylee makes $4 per hour at her job, and she receives a $0.25 raise each month.
    13·1 answer
  • A demolition ball weighs 2 tons. What is the equivalent weight in ounces?
    13·1 answer
  • Is the constant of proportionally in gallons per minute the same for every row? What does this say about the relationship of the
    8·1 answer
  • Lesson 8.8: Angle Relationship
    9·1 answer
  • The sum of twice a number and right is equal to negative eighteen .find the number
    5·2 answers
  • Hello! Please help if you’re able to :D!!
    10·1 answer
  • What is the interquartile range of the following set <br><br> Please help
    14·1 answer
  • PLEASE HELP!! I’ll give brainlest or whatever it’s called
    14·1 answer
  • Which could be the missing data item for the given set of data if the median of the complete data set is 50?
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!