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
algol [13]
3 years ago
7

Prove that the diagonals of a parallelogram bisect each other. The midpoints are the same point, so the diagonals _____

Mathematics
1 answer:
Molodets [167]3 years ago
8 0

Answer:

Below

Step-by-step explanation:

To prove that the diagonals bisect each other we should prove that they have a common point.

From the graph we notice that this point is E.

ABCD is a paralellogram, so E is the midpoint of both diagonals.

●●●●●●●●●●●●●●●●●●●●●●●●

Let's start with AC.

● A(0,0)

● C(2a+2b,2c)

● E( (2a+2b+0)/2 , (2c+0)/2)

● E ( a+b, c)

●●●●●●●●●●●●●●●●●●●●●●●●

BD:

● B(2b,2c)

● D(2a,0)

● E ( (2a+2b)/2 , 2c/2)

● E ( a+b ,c)

●●●●●●●●●●●●●●●●●●●●●●●●●

So we conclude that the diagonals bisect each others in E.

You might be interested in
In triangle KLM, if K is congruent to L, KL = 9x - 40, LM = 7x - 37, & KM = 3x + 23, find x & the measure of each angle.
Dennis_Churaev [7]

Answer: x = 15, ∠K = 45.7°, ∠L = 45.7°, ∠M = 88.6°

<u>Step-by-step explanation:</u>

Since ∠K ≅ ∠L, then ΔKLM is an isoceles triangle with base KL

 KM ≅ LM

3x + 23 = 7x - 37

       23 = 4x - 37

       60 = 4x

        15 = x

KM = LM = 3x + 23

               = 3(15) + 23

               = 45 + 23

               = 68

KL = 9x - 40

    = 9(15) - 40

    = 135 - 40

    = 95

Next, draw a perpendicular bisector KN from K to KL. Thus, N is the midpoint of KL and ΔMNL is a right triangle.

  • Since N is the midpoint of KL and KL = 95, then NL = 47.5
  • Since ∠N is 90°, then NL is adjacent to ∠l and ML is the hypotenuse

Use trig to solve for ∠L (which equals ∠K):

cos ∠L = \frac{adjacent}{hypotenuse}

cos ∠L = \frac{47.5}{68}

      ∠L = cos⁻¹ (\frac{47.5}{68})

      ∠L = 45.7  

Triangle sum Theorem:

∠K + ∠L + ∠M = 180°    

45.7 + 45.7 + ∠M = 180

       91.4     + ∠M = 180

                      ∠M = 88.6

       

7 0
3 years ago
Find the radius of the circle whose equation is (x + 5)2 + (y + 8)2 = 16
Oxana [17]

The radius is 4.

Find the radius of the circle whose equation is (x + 5)2 + (y + 8)2 = 16

6 0
3 years ago
Solve the system by the elimination method.
Vika [28.1K]
10x + 2y - 6 = 0

Multiply 5x + y - 3 = 0 by 2

2(5x + y - 3 = 0) = 10x + 2y - 6 = 0
7 0
3 years ago
Read 2 more answers
SOS HELP ASAP
Nitella [24]

Answer:

The answer would be C

Step-by-step explanation:

The only logical reason would be positive because the parabola is opening up. The average rte of change is opening 0.5 per square

7 0
3 years ago
15 is what percent of 90?​
Alika [10]
15 is 16.66666 percent of 90.
7 0
3 years ago
Read 2 more answers
Other questions:
  • Find the missing number according to the associative property <br><br> (20×5)×11= 20×(11×______)
    14·1 answer
  • Given a random sample of 85 people attending a workshop, 63 of the respondents said the workshop was useful. What is the sample
    7·2 answers
  • In a city, 15% of the bus riders with a monthly pass are students. In a random sample of 50 bus riders with monthly passes, 12 a
    5·1 answer
  • What is 24(a-41) +65 - 14
    9·1 answer
  • X2 + 2x + 5 = 0<br> The discriminant
    5·1 answer
  • -r/2=5<br><br> what does r equal
    14·1 answer
  • Write an equation that has an a-value of -2, a b-value of 1, and a c-value of 3.
    5·1 answer
  • -(1+7 x) – 61–7 – x)= 36
    8·1 answer
  • From 1990 to 2000, the number of visits by the people to Bryce Canyon National Park increased by about 23.9 thousand visits per
    9·1 answer
  • (x - 1)(x + 5) = x² + 4x – 2<br><br> Step by step if possible please
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!