Ask question

Ask question

All categories

3 years ago

9

Mary states, If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle. Decide if her statement i

s true or false?

2 answers:

Mila [183]3 years ago

8 0

The answer for apex would be true.

Darina [25.2K]3 years ago

7 0

Answer:

True

Step-by-step explanation:

Let us consider a parallelogram ABCD in which AB=CD and AD=BC.

Now, from ΔABC and ΔBAD, we have

AD=BC (Opposite sides of parallelogram)

BD=AC (Given)

AB=BA (common)

Thus, by SSS rule of congruency,

ΔABC≅ΔBAD.

Now, by corresponding parts of congruent triangles, we have

∠ABC=∠BAD.

But, we know that ∠ABC and ∠BAD forms the corresponding angle pair, thus ∠ABC+∠BAD=180°

⇒2∠ABC=180

⇒∠ABC=90°

Since they are interior angles of parallel lines AC and BC on the same side of their common secant AB. They are therefore both right, and ABCD is a rectangle.

Hence, the statement If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle is true.

You might be interested in

PLEASE HELP ME WITH THIS QUESTION ITS URGENT!!!

Alex Ar [27]

Start by distributing the exponent to each of the terms in $(2u)^{3}$ . This will become $2^{3} u^{3}$ , and $2^{3} =8$ . Now, the expression is:

$\frac{2u^{3} v^{2} }{8u^{3} * u^{2} }$ .

We can now simplify the bottom to read: $8u^{5}$ because when multiplying variables raised to an exponent, we add the exponents. The expression now looks like:

$\frac{2u^{3} v^{2} }{8u^{5} }$

The 2/8 simplifies to 1/4:

$\frac{u^{3} v^{2} }{4u^{5} }$

Now, we have two u terms on the top and bottom. When dividing variables raised to an exponent, we subtract the exponents. However, since 3-5=-2, the term will be on the bottom to avoid the negative exponent. The final answer is:

$\frac{v^{2} }{4u^{2} }$

Hope this makes sense!!

4 0

3 years ago

Find the range of the data in the box plot below.

kifflom [539]

Answer:

16

Step-by-step explanation:

22-6=16 ;0

3 0

2 years ago

Raquel has created a program for a robot. The robot travels 10 meters and stops. The program is designed for wheels that are 2.5

Grace [21]

Answer:

Raquel should adjust the number of rotations to 115.81 rotations

Step-by-step explanation:

step 1

Find the circumference of the wheels that are 2.5 cm in diameter

The circumference is equal to

$C=2\pi r$

we have

$r=2.5/2=1.25\ cm$

assume

$\pi =3.14$

substitute

$C=2(3.14) (1.25)$

$C=7.85\ cm$

step 2

Find the number of rotations

Divide 10 meters by the circumference

$10\ m=1,000\ cm$

$1,000/7.85=127.39\ rotations$

step 3

For a diameter of 2.75 cm find how should she adjust the number of rotations so that the robot travels the same distance

Find the circumference of the wheels

The circumference is equal to

$C=2\pi r$

we have

$r=2.75/2=1.375\ cm$

assume

$\pi =3.14$

substitute

$C=2(3.14) (1.375)$

$C=8.635\ cm$

step 4

Find the number of rotations

Divide 10 meters by the circumference

$10\ m=1,000\ cm$

$1,000/8.635=115.81\ rotations$

3 0

3 years ago

I need math help. I don’t understand the question.

makkiz [27]

Answer:

A.) 132.3 mm Hg

B.) 49 years old

Step-by-step explanation:

$P= 0.006y^{2} -0.01y+119$

P = blood pressure

y = age in years

A.) Solution

To find: P

Given: y = 48

$P= 0.006y^{2} -0.01y+119$

P = 0.006 x 48 x 48 - 0.01 x 48 + 119

P = 0.006 x 2,304 - 0.48 + 119

P = 13.824 - 0.48 + 119

P = 132.344 ⇒ 132.3

B.) Solution

To find: y

Given: P = 132.92

$P= 0.006y^{2} -0.01y+119$

$132.92= 0.006y^{2} -0.01y+119$

$0.006y^{2} -0.01y-13.92$

.......................................................

Answer: 49 years old

7 0

2 years ago

Which of the following correctly expresses the number below in scientific

frosja888 [35]

Answer:

E. 6.28 x 10^-6

Step-by-step explanation:

7 0

3 years ago