All categories

2 years ago

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

Mathematics

2 answers:

brilliants [131]2 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

ioda2 years ago

6 0

Answer:

∠STP ≅ ∠QTR

Step-by-step explanation:

You might be interested in

Which of the following is the expansion of (3c + d2)6?

vovangra [49]

Answer: Option A) $729c^6 + 1,458c^5d^2 + 1,215c^4d^4 + 540c^3d^6 + 135c^2d^8 + 18cd^{10} + d^{12}$ is the correct expansion.

Explanation:

on applying binomial theorem, $(a+b)^n=\sum_{r=0}^{n} \frac{n!}{r!(n-r)!} a^{n-r} b^r$

Here a=3c, $b=d^2$ and n=6,

Thus, $(3c+d^2)^6=\sum_{r=0}^{6} \frac{6!}{r!(6-r)!} (3c)^{n-r} (d^2)^r$

⇒ $(3c+d^2)^6= \frac{6!}{(6-0)!0!} (3c)^{6-0}.(d^2)^0+\frac{6!}{(6-1)!1!} (3c)^{6-1}.(d^2)^1+\frac{6!}{(6-2)!2!} (3c)^{6-2}.(d^2)^2+\frac{6!}{(6-3)!3!} (3c)^{6-3}.(d^2)^3+\frac{6!}{(6-4)!4!} (3c)^{6-4}.(d^2)^4+\frac{6!}{(6-5)!5!} (3c)^{6-5}.(d^2)^5+\frac{6!}{(6-6)!6!} (3c)^{6-6}.(d^2)^6$

⇒ $(3c+d^2)^6= \frac{6!}{(6-)!0!} (3c)^6.d^0+\frac{6!}{(5)!1!} (3c)^5.d^2+\frac{6!}{(4)!2!} (3c)^4.d^4+\frac{6!}{(6-3)!3!} (3c)^3.d^6+\frac{6!}{(2)!4!} (3c)^2.d^8+\frac{6!}{(1)!5!} (3c).d^{10}+\frac{6!}{(0)!6!} (3c)^0.d^{12}$

⇒ $(3c+d^2)^6=(3c)^6.d^0+\frac{720}{120} (3c)^5.d^2+\frac{720}{48} (3c)^4.d^4+\frac{720}{36} (3c)^3.d^6+\frac{720}{48} (3c)^2.d^8+\frac{720}{120} (3c).d^{10}+.d^{12}$

⇒ $(3c+d^2)^6=729c^6 + 1,458c^5d^2 + 1,215c^4d^4 + 540c^3d^6 + 135c^2d^8 + 18cd^{10} + d^{12}$

3 0

2 years ago

Read 2 more answers

Please help I will give brainliest

lutik1710 [3]

Answer:

Angle PQW is equal to 35 degrees

Step-by-step explanation:

Angle PQW = 36x - 1

Angle WQR = 134x

Angle PQR = 169 degrees

To find angle PQW, Set Angles PQR and WQR to PQW. The equation should look like this:

PQR - WQR = PQW

Substitute in the values

169 - 134x = 36x - 1

Now add 134x to both sides and add 1 to both sides.

170 = 170x

Now divide 170 from both sides

x = 1

Plug x into angle PQW

36(1) - 1 = 35

6 0

2 years ago

An investor has $ 500000 to spend. There investments are being considered, each having an expected annual interest rate. The int

enyata [817]

That's a lot of money and words. I don't appreciate this. I would probably just break down and cry tbh

8 0

2 years ago

In the figure below, what is the value of angle Z?

Hoochie [10]

Answer:

=2.83 the second option

Step-by-step explanation:

Using the trigonometric ratios we can find the sides of the triangle with the acute angles.

In the triangle provided we will use COSINE

Cos ∅=adjacent/hypotenuse

Let us substitute with the values in the question into the formula.

Tan 45 =2/x

x=2/Cos 45

=2.83 units

3 0

1 year ago

Read 2 more answers

On a state map, a cartographer plots Texmath at coordinates (2, 2) and Lonestar Village at coordinates (9, 16). How far is it fr

Digiron [165]

Since two points are given, we can use the distance formula in order to know hpw far is it from Texmath to Lonestar Village. Distance formula is written as

Distance = $\sqrt{ ( x_{2} - x_{1} )^{2} +(y_{2} - y_{1} )^{2} }$

Substituting the values, we have:

Distance = $\sqrt{ ( 9-2 )^{2} +(16-2)^{2} }$

= $\sqrt{7^2 +14^2}$

= √245 = 15.65 units

7 0

2 years ago

Read 2 more answers