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

Answers

Answer 1

The missing statement which is statement 6 is; △AMB ≅ △CMB and ≅ △CMD ≅ △AMD

How to carry out a two column proof?

We have been given several statements and reasons in the given two column proof to prove that ABCD is a rhombus.

Now, the only missing parameter is statement 6 which has its' reason as SAS congruency theorem.

From all the reasons and statements given before statement 6, we can arrive at the conclusion that;△AMB ≅ △CMB and ≅ △CMD ≅ △AMD

Read more about two column proof at; https://brainly.com/question/1788884

#SPJ5

Answer 2

Answer:

B: △AMB ≅ △CMB ≅ △CMD ≅ △AMD

Step-by-step explanation:

edg


Related Questions

The three interior angle measures of this triangle are x= ___, y= ___, and z= ___.

Answers

Answer:

∡x = 30°

∡y = 70°

∡z = 80°

Step-by-step explanation:


Does the graph above show a relation, a function, both a relation and a function, or neither a relation nor a function?

Answers

Answer:

The graph shows a relation and a function

Step-by-step explanation:

Because there is one value of y for every value of x, this is a relation and a function.

Answer:

relation because the x does not repeat

In Mr. Jegou’s neighborhood 35% of the houses are blue. Write the percent that do not live in blue houses as a decimal and a fraction in simplest form

Answers

Answer:

65%

Step-by-step explanation:

65% + 35%=100%

Before the florist has a chance to finish the bouquets, a large order is
placed. After the order, only 85 roses and 163 peonies remain. How many
regular bouquets and mini bouquets can the florist make now?

Answers

Answer: 8 regular and 15 mini bouquets

Step-by-step explanation: yw <3

To get the correct color, Johan mixed 3 1/4 quart of white paint, 1 2/4 quart of blue paint, and 2 3/4 quart of green paint. How much paint did Johan make? * answer to this problem hat is what i need

Answers

Answer:

7 1/2 quart of paint

Step-by-step explanation:

To get the correct color, Johan mixed 3 1/4 quart of white paint, 1 2/4 quart of blue paint, and 2 3/4 quart of green paint. How much paint did Johan make? *

The above question is solved as:

3 1/4 quart + 1 2/4 quart + 2 3/4 quart

Lowest common denominator = 4

3 + 1 + 2 + ( 1/4 + 2/4 + 3/4)

= 6 + ( 1 + 2 + 3/4)

=( 6 + 6/4) quart

= 6 + 1 2/4 quart

= 7 2/4 quart of paint

= 7 1/2 quart of paint

Therefore, Johan made 7 1/2 quart of paint

Drag the tiles to the boxes to form correct pairs.
Not all tiles will be used.
Match each binomial with its factors.​

Answers

Answer:

1 .4x2-9= 2x+3,2x-3

2 .16x2-1=4x-1,4x+1

3 .16x2-4=4(2x+1)(2x-1)

4 .4x2-1=(2x+1)(2x-1)

Step-by-step explanation:

16x² − 1  = (4x − 1)(4x + 1) ;  16x² − 4  = 4(2x + 1)(2x − 1); 4x² − 1  = (2x + 1)(2x − 1) ;

4x² − 9 = (2x + 3)(2x − 3)

16x² − 1  is the difference of squares.  This is because 16x² is a perfect square, as is 1.  To find the factors of the difference of squares, take the square root of each square; one factor will be the sum of these and the other will be the difference.

The square root of 16x² is 4x and the square root of 1 is 1; this gives us (4x-1)(4x+1).

16x² − 4 is also the difference of squares.  The difference of 16x² is 4x and the square root of 4 is 2; this gives us (4x-2)(4x+2).  However, we can also factor a 2 out of each of these binomials; this gives us

2(2x-1)(2)(2x+1) = 2(2)(2x-1)(2x+1) = 4(2x-1)(2x+1)

4x² − 1  is also the difference of squares.  The square root of 4x² is 2x and the square root of 1 is 1; this gives us (2x-1)(2x+1).

4x² − 9 is also the difference of squares.  The square root of 4x² is 2x and the square root of 9 is 3; this gives us (2x-3)(2x+3).

Answer:

Have a great rest of your day :)

Step-by-step explanation:

need help ASAP !!!


[tex] \sqrt{18 \times 18 \times 4} [/tex]

Answers

Answer:

36

Step-by-step explanation:

The first step to solving this equation is multiplying. Multiply the numbers on the inside of the square root.

18 × 18 × 4 = 1296

Now, you are going to find the square root of 1296.

[tex]\sqrt{1296}[/tex] = 36

You now have your final answer.

I hope this makes sense and is easy to understand. Please let me know if you need any more help. Have a great day! :]

Answer:

Step-by-step explanation:

[tex]\sqrt{18(18)(4)}\\ \\ \sqrt{2(3^2)2(3^2)2^2}\\ \\ \sqrt{2^4(3^4)}\\ \\ 2^2(3^2)\\ \\ 4(9)\\ \\ 36[/tex]

The measure of an angle is 39°. What is the measure of its complementary angle?

Answers

Answer:

51 degrees

Step-by-step explanation:

Complementary angles are two angles whose sum is (90degrees). If one is given an angle measure and needs to find its complementary angle, then all one has to do is subtract the given angle measure from (90degrees).

90 - 39 = 51

Answer:

51°

Step-by-step explanation:

Complementary angles add to 90°.

If one of them is 39°, then the other is:

90° - 39° = 51°

Julie wants to attend a two-year college that has an annual tuition of $8,600. Julie earned a grant of $1,600 for each year and has saved $5,980 for college. How much more does she need to pay the tuition for both years?

Answers

Answer: $8,020

Steps:
$8,600 * 2yrs = $17,200

$1,600 * 2yrs = $3200

$3200 + $5980 = $9180

$17,200 - $9,180 = $8,020

She need to save $8, 020 more

I would appreciate brainliest if This was helpful and correct! :)

CAN SOMEONE PLEASE HELP WITH THIS ILL GIVE YOU BRAINLY IF YOU GET IT RIGHT !!!!

Answers

Answer:

20%

Step-by-step explanation:

4+5+3 equals 12. in all, all of the frequencies combined is 30. because of that, it equals 20%. pls give brainliest

Did I do the math right? Is it D?

Answers

Answer:

i think

Step-by-step explanation:

help this is due today ;::

Answers

Answer: C- 17

Step-by-step explanation:

Write an equation for the hanger diagram and then us the sketch to show how to solve the equation algebraically.

Answers

Step-by-step explanation:

Since there are 3 w's and a 1 on one side and 7 1's on the other and the hanger diagram shows they are even, we can set them equal to each other.

3w + 1 = 7 Subtract 1 from both sides

3w = 6 Divide 3 from both sides

w = 2

Help...Need the answer right away

Answers

Answer:

45 cm

Step-by-step explanation:

Area of a triangle:

A = 1/2bh

b = 3 + 2 = 5

A = 1/2(5)(6)

A = 15

Area of a rectangle:

A = bh

A = 12*2.5

A = 30

Combined:

30 + 15 = 45

The sailboat has 2 right angle triangles and a rectangle

First lets find the area of the rectangle then each one of the triangles

Area of rectangle = Length × Height

Area of rectangle = 12 × 2.5

Area of rectangle = 30 cm²

Now lets find the area of triangle on the right,

Area of triangle = Height × base × [tex]\frac{1}{2}[/tex]

Area of triangle = 6 × 3 × [tex]\frac{1}{2}[/tex]

Area of triangle = 18 × [tex]\frac{1}{2}[/tex]

Area of triangle = [tex]\frac{18}{2}[/tex]

Area of triangle = 9 cm²

Now lets find the area of the triangle on the left,

Area of triangle = Height × base × [tex]\frac{1}{2}[/tex]

Area of triangle = 6 × 2 × [tex]\frac{1}{2}[/tex]

Area of triangle = 12 × [tex]\frac{1}{2}[/tex]

Area of triangle = [tex]\frac{12}{2}[/tex]

Area of triangle = 6 cm²

Now lets find the total area of the sailboat,

Total area = Area of rectangle + Area of triangle on the right + Area of triangle on the right

Total area = 30 + 9 + 6

Total area = 39 + 6

Total area = 65 cm²

Therefore the total area of the sailboat is 65 cm²

Happy to help :)

If you need anymore help, feel free to ask

Stephanie puts 30 cubes in a box. The cubes are inch on each side. The box holds 2 layers
with 15 cubes in each layer. What is the volume of the box?

Answers

Answer:

[tex] 11.25\: {in}^{3} [/tex]

Step-by-step explanation:

Since, box contains two layers of cubes and each layer has 15 cubes.

So, length = 15*1/2 in = 7.5 in,

width = 3*1/2 in = 1.5 in

height = (1/2 + 1/2) = 1 inch

Volume of box = lbh

= 7.5* 1.5 *1

= 11.25 cubic inches

Simplifying Radicals
in simplest radical form
Ra...
a.
v-117
b. V12 - 27 + 2 V3
c.
V3 * 142

Answers

Answer:

Step-by-step explanation:

PLEASE HELP I WILL GIVE BRAINLIEST PLEASE 20 POINTS

Answers

9514 1404 393

Answer:

  [tex]\begin{cases}3x+12&\text{if }x>-4\\0&\text{if }x=-4\\-3x-12&\text{if }x<-4\end{cases}[/tex]

Step-by-step explanation:

The absolute value function negates its argument when its argument is negative. The expression 3x+12 will be negative when ...

  3x +12 < 0

  x +4 < 0

  x < -4 . . . . . makes the absolute value function change its argument's sign

Using this fact, we can divide the domain into intervals below -4, at -4, and above -4. The above answer shows the function value in each domain interval.

How many faces does the solid figure made from the net below have?


43

Answers

Answer:

43

Step-by-step explanation:

HARD QUESTION 100 POINTS

Answers

Answer:

2

There is a picture the website is Math-way I use it all the time to help out or just to check my answers.

Answer:

i was abt to answer but too late prolly

Step-by-step explanation:

if u still wanna know,

R = 21 ft. find the radius or diameter ​

Answers

Answer:

Radius = 21 ft

Diameter = 42 ft

Step-by-step explanation:

Answer:

radius is 10.5 ft.

Step-by-step explanation:

bc I said so

The graph of an equation is shown below:

Answers

Answer:

D, or (-3,2)

Step-by-step explanation:

Because the point (-3,2) is on the line of the equation shown, it is a solution. You can also notice that none of the other options are on the line and use the process of elimination.

Determine if the two triangles are congruent. If yes, which theorem proves their congruence?

Answers

Answer:

Not congruent.

The Angle-Side-Side Postulate does not exist because an angle and two sides does not guarantee that two triangles are congruent. If two triangles have two congruent sides and a congruent non included angle, then triangles are NOT NECESSARILLY congruent.

Step-by-step explanation:

I got one question wrong on a test, but my grade was 96%. Why is 24/25 96% and not 99% if I only got one thing wrong?

Answers

Answer:

Cause if u multiply 24/25 x 4 u get 96 and 100 not 99 and 100

Step-by-step explanation:

Answer:

Step-by-step explanation:

x : 100 = 24: 25

x = (24 x 100)/25 = 96%

find the value of given expression

[tex] \sqrt{395 \times 395} [/tex]
anyone wanna play chess ?​

Answers

Answer:

√{395×395}=√395²=395 is your answer

Answer:

[tex] \sqrt{395 \times 395} [/tex][tex] \sqrt{395} \times \sqrt{395} [/tex][tex]395[/tex]

I'm so confused on this can someone please help and explain it to me!

Answers

Answer:

A's coordinates are:

A. (-4, 3)

Step-by-step explanation:

Because the x  always goes first,

So that will mean -4 will go first.

After you have -4 down, you will see that A's point on the graph is (-4, ?)

To answer the ?, you will have to check the y.

Because remember, The x-coordinate always comes first, followed by the y-coordinate.

So, it will be (-4, 3)

and 3 will be the fill in for y.

I hope this helps     :)

Which graph represents the solution set of - 4x - y<-6?

Answers

Answer:

Step-by-step explanation:

Where are the graphs?

Q. A dice shows the numbers 1 through 12, with one number showing each time the die is rolled. What is the probability of rolling a 7?

Answers

Answer:

1/12

Step-by-step explanation:

The total number is 12 (assuming the dice would be rolled 12 times) 7 is a number in the range and it will appear once in the 12 rolls because each number shows each time. 1 (how many times 7 will show)/ 12(total number of rolls)

Probability of [tex]7[/tex] when a dice (showing numbers 1 throught 7) is thrown is equal to [tex]\boldsymbol{\frac{7}{12}}[/tex] as a dice is rolled.

Define probability.

Probability refers to chances of occurrence of any event.

Value of probability lies in the interval [tex]\boldsymbol{\left [ 0,1 \right ]}[/tex]

Total number of numbers on a dice [tex]=12[/tex]

Probability is equal to number of favorable outcomes divided by the total number of outcomes.

Probability of [tex]7=\frac{7}{12}[/tex]

Find out more information about probability here:

https://brainly.com/question/11234923?referrer=searchResults

A triangle has side lengths of 16 cm and 7 cm. Which could be the value of the third side, 28 cm or 19 cm?

The Value _______ cm is the value of the third side.

Drop down options:

28
19

Answers

Answer:

19

Step-by-step explanation:

by pythagoras theorm

19 i think, i’m more of a visual person lol

. Larry solved this equation. 3(2-3)= x Which representation could Larry have used to solve this equation?

Answers

Answer:

x = -3

Step-by-step explanation:

Given the expression solved by Larry as;

3(2-3) = x

We are to find the equivalent expression x

Using the distributive law;

3(2) - 3(3) = x

6 - 9 = x

-3 = x

Swap

x = -3

Hence Larry could use the distributive law to solve the expression

Which of the following equations models the same function as 2x-3y=6 A, y=2/3x-15 B, y=-2/3x-2 C, y=-2/3x-15 D, y=2/3x-2

Answers

Answer:

D. y= 2/3x-2

Step-by-step explanation:

y=6-2x/-3

-2+2/3x

2/3x-2=y

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