All categories

3 years ago

If quadrilateral PQRS is a rectangle, then which of the following is true?

Mathematics

2 answers:

brilliants [131]3 years ago

8 0

∠STP ≅ ∠QTR is the True statement ⇒ answer C

Step-by-step explanation:

In any rectangle

1. Each two opposite sides are equal and parallel

2. The measure of its vertex angles is 90°

3. The two diagonals are equal

Now lets find the true statements

∵ PQRS is a rectangle

∴ PS = QR ⇒ opposite sides

∴ PQ = SR ⇒ opposite sides

∴ PR = QS ⇒ diagonals

A. ∠PSQ ≅ ∠QSR

∵ The diagonals of the rectangle do not bisect the vertex angles

∴ AQ does not bisect angle S

∴ m∠PSQ ≠ m∠QSR

∴ ∠PSQ not congruent ∠QSR

∠PSQ ≅ ∠QSR ⇒ False

B. segment SR ≅ segment RQ

∵ SR and RQ are two adjacent sides

∵ The adjacent side in the rectangle not equal

∴ SR ≠ QR

∴ segment SR not congruent to segment RQ

segment SR ≅ segment RQ ⇒ False

C. ∠STP ≅ ∠QTR

∵ PR intersects QS at point T

∴ m∠STP = m∠QTR ⇒ vertically opposite angles

∴ ∠STP ≅ ∠QTR

∠STP ≅ ∠QTR ⇒ True

D. segment PS ≅ segment PR

∵ PS is a side in the rectangle

∵ PR is a diagonal in the rectangle

∵ The side of the rectangle not equal the diagonal of the rectangle

∴ PS ≠ PR

∴ segment PS not congruent to segment PR

segment PS ≅ segment PR ⇒ False

∠STP ≅ ∠QTR is the True statement

Learn more:

You can learn more about rectangle in brainly.com/question/6594923

#LearnwithBrainly

ioda3 years ago

6 0

Answer:

∠STP ≅ ∠QTR

Step-by-step explanation:

You might be interested in

Alberto recorded the heights of the basketball team members.

Alex777 [14]

I don't know the real answer, but I think it is C. (I am sorry if I am wrong).

8 0

4 years ago

Read 2 more answers

The midpoint of AB is M(3, 3). If the coordinates of A are (2, -1), what are the

Vika [28.1K]

Step-by-step explanation:

Hey there!!

It's so simple.

While finding the coordinates of any point if the midpoint is there it will be much easier. You must remember the midpoint formulae.

Let's simply work with it.

Here, A (2,-1) and midpoint M(3,3) are given.

Let another coordinate be B(x,y).

By midpoint formulae,

$midpoint(x.y) = \frac{x1 + x2}{2} ,\frac{y1 + y2}{2}$

Putting their values,

$m(3 , 3) = \frac{2 + x}{2} , \frac{ - 1 + y}{2}$

As they are equal, equating with their corresponding elements we get,

$3 = \frac{2 + x}{2}$

6= 2 + x

x = 6-2

Therefore, the value of a is 4.

Again,

$3 = \frac{ - 1 + y}{2}$

6 = -1 + y

Therefore, the value of y is 7.

Therefore, the coordinates are B (4,7)

Hope it helps....

7 0

3 years ago

Read 2 more answers

estimate the number of cubic yards of gravel needed to fill a 26' x 20' garage with a layer of gravel that is 18 inches deep, ro

Gemiola [76]

$26 \times 20 + 18$

5 0

3 years ago

Please tell me how to find the Slope of lines, (or do one for me) [I’ll try to help you back]

zheka24 [161]

The slope of a line often referred to as the ( $\frac{rise}{run}$ ) is the rate of change in a line. It can be found using the following formula.

$\frac{y_2-y_1}{x_2-x_1}$

Where ( $x_1,y_1$ ) and ( $x_2,y_2$ ) are points on the line. For each problem, substitute the points on the line into the formula and solve for the slope.

1. $\frac{1}{2}$

(0, 2), (-2, 1)

$=\frac{1-2}{-2-0}\\\\=\frac{-1}{-2}\\\\=\frac{1}{2}$

2. 2

(-2, -1), (0, 3)

$=\frac{3-(-1)}{0-(-2)}\\\\=\frac{3+1}{0+2}\\\\=\frac{4}{2}\\\\=2$

3. 4

(1, 0), (2, 4)

$=\frac{4-0}{2-1}\\\\=\frac{4}{1}\\\\=4$

4. 1

(6, 2), (2, -2)

$=\frac{-2-2}{2-6}\\\\=\frac{-4}{-4}\\\\=1$

5. $\frac{3}{5}$

(-1, 1), (4, 4)

$=\frac{4-1}{4-(-1)}\\\\=\frac{3}{4+1}\\\\=\frac{3}{5}$

6. $\frac{1}{3}$

(-7, 4), (2, 1)

$=\frac{4 -1}{2-(-7)}\\\\=\frac{3}{2+7}\\\\=\frac{3}{9}\\\\=\frac{1}{3}$

7. 0

(5, -3), (-2, -3)

$=\frac{-3-(-3)}{-2-5}\\\\=\frac{-3+3}{-7}\\\\=0$

8. $\frac{7}{5}$

(-3, 2), (2, 7)

$=\frac{7-2}{2 - (-3)}\\\\=\frac{7}{2+3}\\\\=\frac{7}{5}$

9. 8

(2, 16), (3, 24)

$=\frac{24-16}{3-2}\\\\=\frac{8}{1}\\\\=8$

4 0

3 years ago

Please help me with this question.

frez [133]

Use cross multiply and divide where the first fraction is the percent over 100. and the second is blank over the amount of students. solve. work shown above.

3 0

3 years ago