Which of the following pairs of values for x and y would justify the claim that the two triangles are congruent?

In parallelogram QRST QS RT Is QRST a rectangle ?

fomenos

Answer:

The correct option is A.

Step-by-step explanation:

It is given that the QRST is a parallelogram and the diagonals QS and RT are congruent.

According to the property of parallelogram if the length of diagonals are same, then the parallelogram is rectangle. We can also prove it.

Let QRST be an parallelogram and QS=RT.

In triangles QRT and RQS.

$RT=QS$ (Diagonals)

$QR=QR$ (Common side)

$QT=RS$ (Opposite sides of the parallelogram are same)

So by SSS rule of congruence, triangle QRT and triangle RQS are congruent.

By CPCT,

$\angle R=\angle Q$

Since the sum of two consecutive angles of a parallelogram is 180 degree.

$\angle R+\angle Q=180$

$2\angle R=180$

$\angle R=90$

Therefore the measure of angle R and angle Q are 90 degree.

Similarly in triangle QST and RTS,

$RT=QS$ (Diagonals)

$ST=ST$ (Common side)

$QT=RS$ (Opposite sides of the parallelogram are same)

So by SSS rule of congruence, triangle QST and RTS are congruent.

By CPCT,

$\angle S=\angle T$

Since the sum of two consecutive angles of a parallelogram is 180 degree.

Therefore the measure of angle S and angle T are 90 degree.

Since the measure of all interior angles of QRST are 90 degree, therefore the parallelogram QRST is a rectangle.

6 0

4 years ago

Read 2 more answers

Quan's last paycheck shows that he eamed $210.00 for 24 hours of work. What is his hourly rate of pay?

Mariana [72]

Answer:

8.57 explanation:

Step-by-step explanation: If Quan gets 210 dollars every 24 hours and you want to find the amount he gets every hour all you have to do is do 210 divided by 24 which you will get 8.75. So every hour he gets $8.75 every hour for his work

7 0

3 years ago

Read 2 more answers

Find out the number of combinations and the number of permutations for 8 objects taken 6 at a time. Express your answer in exact

umka2103 [35]

Solution:

The permutation formula is expressed as

$\begin{gathered} P^n_r=\frac{n!}{(n-r)!} \\ \end{gathered}$

The combination formula is expressed as

$\begin{gathered} C^n_r=\frac{n!}{(n-r)!r!} \\ \\ \end{gathered}$

where

$\begin{gathered} n\Rightarrow total\text{ number of objects} \\ r\Rightarrow number\text{ of object selected} \end{gathered}$

Given that 6 objects are taken at a time from 8, this implies that

$\begin{gathered} n=8 \\ r=6 \end{gathered}$

Thus,

Number of permuations:

$\begin{gathered} P^8_6=\frac{8!}{(8-6)!} \\ =\frac{8!}{2!}=\frac{8\times7\times6\times5\times4\times3\times2!}{2!} \\ 2!\text{ cancel out, thus we have} \\ \begin{equation*} 8\times7\times6\times5\times4\times3 \end{equation*} \\ \Rightarrow P_6^8=20160 \end{gathered}$

Number of combinations:

$\begin{gathered} C^8_6=\frac{8!}{(8-6)!6!} \\ =\frac{8!}{2!\times6!}=\frac{8\times7\times6!}{6!\times2\times1} \\ 6!\text{ cancel out, thus we have} \\ \frac{8\times7}{2} \\ \Rightarrow C_6^8=28 \end{gathered}$

Hence, there are 28 combinations and 20160 permutations.

7 0

1 year ago

keiko, chang, and scott sent a total of 130 text messages over their cell phones during the weekend. Scott sent 10 fewer message

Olenka [21]

Keiko sent 30 text messages Scott sent 20 text messages chang sent 80

8 0

4 years ago

Find the volume of the cone. Use 3.14 for n. Round to the nearest tenth.

enyata [817]

Answer:

$1590.6cm {}^{3}$

Step-by-step explanation:

$volume \: of \: a \: cone \: v = \frac{1}{3}\pi \: r {}^{2} h \\ radius = \frac{diameter}{2} = \frac{15}{2} = 7.5 \\ v = \frac{1}{3} \times 3.42 \times (7.5) {}^{2} \times 27 \\ v = \frac{3.142 \times 7.5 \times 7.5 \times 27}{3} \\ v = \frac{4771.9125}{3} = 1590.6375 \\ v = 1590.6cm {}^{3} (approximatly) \\ please \: rate \: and \: mark \: brainliest$

7 0

2 years ago