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Zepler [3.9K]
3 years ago
6

The figure below shows a rectangle ABCD having diagonals AC and DB: A rectangle ABCD is shown with diagonals AC and BD. Anastasi

a wrote the following proof to show that the diagonals of rectangle ABCD are congruent: Anastasia's proof: Statement 1: Statement 2: AB = DC (opposite sides of a rectangle are congruent) Statement 3: AC2 = DB2 (from statements 1 and 2) Statement 4: AC = DB (taking square root on both sides of AC2 = DB2) Which statement below completes Anastasia's proof? In triangle ADC and BCD, AB = DC (opposite sides of a rectangle are congruent) In triangle ADC and BCD, AB = DC (opposite sides of a rectangle are parallel) In triangle ADC and BCD, AD = BC (opposite sides of a rectangle are congruent) In triangle ADC and BCD, AD = BC (opposite sides of a rectangle are parallel)
Mathematics
1 answer:
erica [24]3 years ago
7 0

Answer:In triangle ADC and BCD, AD = BC (opposite sides of a rectangle are congruent)


Step-by-step explanation:

As congruent means shapes having the same length and same internal angles.  In the given figure the two statements are already written. The only information about sides AD and BC are missing to complete the proof of congruent diagonals.


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Find the sum of the first 10<br> terms.<br> 40,37,34,31,...
MArishka [77]

Answer:

It seems each number is 3 less than the previous number.

We must sum these 10 numbers

40, 37, 34, 31, 28, 25, 22, 19, 16, 13

The sum would equal the average of the middle 2 numbers times 10.

(28 + 25) / 2 = 53 / 2 = 26.5

We multiply by 10 because there are 10 numbers and this equals

265

Step-by-step explanation:

3 0
4 years ago
Read 2 more answers
Elsa's magic wand can cast 53 spells. Her wand can cast 17fewer spells than her sister Anna's wand, which is a little bigger and
Mademuasel [1]

Answer:

<em> Anna's wand can cast 70 spells</em>

<em></em>

Step-by-step explanation:

Elsa's wand can cast 53 spells

her wand casts 17 fewer cells than her sister Anna's

Amount of spells cast by Anna's wand = ?

We write the question down in the form of an equation

x - 17 = 53

where x is the amount of spells Anna's wand can cast.

we then proceed to solve by collecting like terms to different sides of the equation. We'll have

x = 53 + 17

which leaves us with

x = 70

This means that<em> Anna's wand can cast 70 spells.</em>

4 0
3 years ago
Not good at this need some help
emmasim [6.3K]

Answer:

216 sq. units

Step-by-step explanation:

From the figure, we can see that only one pair of opposite angles are equal. So, the quadrilateral is a kite.

Formula to find the area of a kite:

Area, A = $ \frac{1}{2} \times d_1 \times d_2 $

where, $ d_1 $ and $ d_2 $ are the lengths of the diagonals.

Here, $d_1 = 18 $ units.

And, $ d_2 = 24 $ units.

Therefore, the area A = $ \frac{1}{2} \times 18 \times 24 $

= $ \frac{432}{2} $

= 216 sq. units which is the required answer.

6 0
4 years ago
If the ratio of the sides of two squares is 3:1, what is the ratio of their perimeters?
Anvisha [2.4K]

Answer:

Ratio of the perimeters =3:1

Step-by-step explanation:

We have given that : Ratio of the sides of two squares is 3:1

To find : Ratio of their perimeters

Solution : Let the length of the sides are 3:1 = 3x : x

                  Formula of perimeter of square = 4(side)

Using the formula ,

Perimeter of 1 square = 4×3x= 12x

Perimeter of 2 square = 4×x= 4x

Ratio of the perimeter of 1 square and 2 square = 12x : 4x

                                                                                 = 3 : 1


8 0
3 years ago
All 231 students in math club went on a field trip some rode in vans that held 7 people and some rode on buses that held 25 peop
MariettaO [177]

Answer:

8 vans

7 buses

Step-by-step explanation:

Let there be "b" buses

and "v" vans

Since 7 people is the capacity of vans, the total capacity is

7v

Also, since 25 people is the capacity of 1 bus, the total capacity is

25b

In total 231 people, so we can write our first equation as:

7v + 25b = 231

Now, we know there are 15 vehicles (bus + vans) in total, so we can write our 2nd equation as:

v + b = 15

Now, we solve for v and b. Let's solve the 2nd equation for v and substitute that into 1st and solve for b first:

v + b = 15

v = 15 - b

Now,

7v + 25b = 231\\7(15-b) + 25b = 231\\105-7b+25b=231\\18b=126\\b=7

Hence, there are 7 buses

Since 15 vehicles in total, the number of vans is:

15 - 7 = 8 vans

So,

8 vans

7 buses

8 0
4 years ago
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