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Diagonals AC and BD form right angles at point M in parallelogram ABCD. Prove ABCD is a rhombus.


Parallelogram A B C D is shown. Diagonals are drawn from point A to point C and from point B to point D and intersect at point M. Sides A B and D C are parallel and sides B C and A D are parallel. A square is drawn around point M.



Statements


Reasons

1. ABCD is a parallelogram 1. given

2. ∠AMB, ∠BMC, ∠CMD, and ∠DMA are right angles 2. given

3. ∠AMB ≅ ∠BMC ≅ ∠CMD ≅ ∠DMA 3. right angles are congruent

4. AC bisects BD;

BD bisects AC; 4. diagonals of a parallelogram bisect each other

5. AM ≅ MC, MB ≅ MD 5. definition of a bisector

6. ? 6. SAS congruency theorem

7. AB ≅ BC ≅ CD ≅ DA 7. CPCTC

8. figure ABCD is a rhombus 8. definition of a rhombus

△ABC ≅ △ADC ≅ △BAD ≅ △BCD

△AMB ≅ △CMB ≅ △CMD ≅ △AMD

△ABC ≅ △ADC ≅ △AMD ≅ △BMC

△AMB ≅ △CMD ≅ △BAD ≅ △BCD

Answer:

no error original system so good by

Answer:

y = 1/2x - 2.5

Step-by-step explanation:

(15, 5) and (42, 18.5)

Slope:

m=(y2-y1)/(x2-x1)

m=(18.5 - 5)/(42 - 15)

m = (13.5)/27

m = 1/2

y - y1 = m(x - x1)

y - 5 = 1/2(x - 15)

y - 5 = 1/2x - 7.5

y = 1/2x - 2.5

Answer:

2   or    1/2

Step-by-step explanation:

change in y over change in x

you didnt define what what x and what was y so ill provide both answers and you can figure which is correct

42-15/18.50-5   =27/13.5   =2

18.50-5/42-15    =13.5/27  =1/2

:)

Answer:

It says c = πd

The circumference is π X d (diameter)

on the image the diameter shown on the circle is 14cm

π = 3.14

3.14 X 14cm = 43.96cm

Answer:

slope is negative

m=-1

Step-by-step explanation:

the slope of a line is positive if it passes through Quadrants III and I. The slope is negative if it passes through II and IV.

yes, this line passes through Quadrant I alongside II and IV, but it doesn't pass through Quadrant III (it has to pass through Quadrant III to be positive)

that means that the slope of this line must be negative

We can calculate the slope (m) with this formula:

(y2-y1)/(x2-x1)

we can pick two points- for example, (1,3) and (2,2)

label the points:

x1=1

y1=3

x2=2

y2=2

now substitute into the equation

m=(2-3)/(2-1)

m=-1/1

m=-1

the slope is -1

Hope this helps! :)

Answer:

52cm^2

Step-by-step explanation:

I did the splitting in my head and that's pretty hard to explain like this so, just BTW if your confused on where I got my lengths from.

(7*6) + (5*2)

(42) + (10)

52

I separated them into an almost square and a rectangle, then I found the area of each rectangle and then added them together.

Hopefully this was useful and you didn't have any issues with this!

Answer:

2/5 or 40%

Step-by-step explanation:

.40 is 40 hundredths or 40/100

40/100 can be reduced to 20/50 and reduced again to 10/25 and one more time to 2/5

Percentages are fractions out of 100 so 40/100 would be 40%.

Answer:

Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24...

Step-by-step explanation:

Multiple of any number is a number which can be divided exactly by that number. The Multiples of a number are formed by multiplyng it with other numbers like 1,2,3,etc.

Answer:

14587676

Step-by-step explanation:

Answer:

top right one

Step-by-step explanation:

Answer:

35

Step-by-step explanation:

Answer:

1680.25

Step-by-step explanation:

Answer:

y < 1

Step-by-step explanation:

the value of y in the whole part is less than or equal to 1.

Answer:

where's the question. you gave no information....

Step-by-step explanation:

I don't know what I have to work with...

Answer:

12+8*6

Step-by-step explanation:

Answer:

Jeff bought a canoe for $333.75. The sales tax was 5%. What was his total cost?

Step-by-step explanation:

The total cost of jeff  purchase was approximately $351.27.

Actual Answer:

A (I  THINK )

Answer:

There is a hack in forms that forms gives u the answer hold ctrl + u, and scrool to the bottom he read the part with the question and there will be an answer.

Mark as brainliest if im right good luck!!

Answer C

Step by step: i think its c because i have no idea.

Answer:

u =  21

Step-by-step explanation:

WX = XY because (VW = VY)

WX = u + 42

XY = 3u

u + 42 = 3u

42 = 3u - u

42 = 2u

u = 42 / 2

u = 21

Answer:

u = 21

Step-by-step explanation:

Consider triangle XWV and triange XYV

XV = XV (common)

Angle XVW = Angle XVY (given)

VW = VY (given)

∴triangle XWV ≅ triange XYV (SAS)

∴ XW = XY (corr. sides, ≅ triangles)

u + 42 = 3u

u = 21

Answer:

x^2 + y^2 = 4

Step-by-step explanation:

General for of a circle is x^2 + y^2 = r^2

The circle is centered at the origin and the radius is 2.

Answer:

25.6125

Step-by-step explanation:

since 25 is a whole number, it'd be 25.ˣˣˣˣ

now all you have to do it divide the fraction so 49 ÷ 80 =  0.6125

last step is to add ⇒ 25 + 0.6125 = 25.6125

Answer:

a) KJL = 76⁰

b) LKM = 76/2 = 38⁰

Answer:

∠KJL = 76°

∠LKM = 38°

Step-by-step explanation:

since arc KL = 76°, ∠KJL also = 76° because central angles are congruent to their arcs.

∠LKM = 1/2 arc KL = 1/2(76°) = 38°

eighteen biscuits are made from each cup

Answer:

first 4 terms: 3,1,-1,-3

10th: -35

Step-by-step explanation:

Please mark as brainliest if answer right

Have a great day, be safe and healthy  

Thank u  

XD

Answer:

3, 1, - 1, - 3 and - 15

Step-by-step explanation:

To find the first 4 terms substitute n = 1, 2, 3, 4 into the rule, that is

a₁ = 5 - 2(1) = 5 - 2 = 3

a₂ = 5 - 2(2) = 5 - 4 = 1

a₃ = 5 - 2(3) = 5 - 6 = - 1

a₄ = 5 - 2(4) = 5 - 8 = - 3

The first 4 terms are 3, 1, - 1, - 3

For 10th term substitute n = 10 into the rule

a₁₀ = 5 - 2(10) = 5 - 20 = - 15

Answer: The shapes that have parallel sides would be the blue diamond               (bottom right) and the green trapezoid (top right).

The shapes that have the parallel sides should be blue diamond               (bottom right) and the green trapezoid (top right).

The parallel sides are considered as the two sides or line that should be parallel to one other also it contain the same kind of distance also it never intersected or even touched to one another.

hence, The shapes that have the parallel sides should be blue diamond               (bottom right) and the green trapezoid (top right).

Learn more about sides here: https://brainly.com/question/18190212

Answer:

C

Step-by-step explanation:

process of elimination

Answer:

n=7 and p=2

Step-by-step explanation:

Graph is not given,

we have n=2p+3 and n=5+p

that's 2p+3=5+p

P=5 - 3

P=2

so the solution is n=7 and p=2

Answer:

(2,7)

Step-by-step explanation:

Answer:

n = 15

Step-by-step explanation:

A straight line equals 180 degrees

Angle SWT is congruent to angle XWV meaning:

SWT (55 degrees) = XWV (55 degrees)

Set up an equation:

3n + 80 + 55 = 180

Combine like terms

3n + 135 = 180

Subtract both sides by 135 to isolate variable n

3n = 45

Divide both sides by 3 to isolate variable n

n = 15