Points P, Q, R, and S are collinear. Point Q is between P and R, R is between Q and S, and PQ overbar congruent RS overbar. If PSequals30 and PRequals23, what is the value of QR
Given that points P, Q, R, and S are collinear, and Q is between P and R, and R is between Q and S.
We are also given that PQ ≅ RS and PS = 30 and PR = 23.
Since PQ ≅ RS, we can set up the following equation:
PQ + QR = PR + RS
Substituting the given values:
PQ + QR = 23 + 30
Since PR + RS = PS, we can simplify the equation:
PQ + QR = PS
Substituting the given values:
PQ + QR = 30
We know that PQ + QR = 23 + QR = 30
Subtracting 23 from both sides:
QR = 30 - 23
QR = 7
Therefore, the value of QR is 7.
To find the value of QR, we need to use the fact that PQ and RS are congruent and that PR equals 23 while PS equals 30.
Let's break down the given information:
1. Point Q is between P and R. This means that Q is somewhere between P and R on the collinear line.
2. Point R is between Q and S. This means that R is between Q and S on the collinear line.
3. PQ overbar is congruent to RS overbar. This means that the length of PQ is equal to the length of RS.
4. PR equals 23. This means that the length of PR is 23 units.
5. PS equals 30. This means that the length of PS is 30 units.
Knowing this information, we can set up the equation:
PQ + QR = PR
Since PQ and RS are congruent, we can substitute the value of PQ with RS:
RS + QR = PR
Since PR equals 23, we can substitute the value:
RS + QR = 23
Substituting the value of PS with 30:
RS = 30
Now we can substitute this value into the equation:
30 + QR = 23
By subtracting 30 from both sides, we get:
QR = 23 - 30
QR = -7
Therefore, the value of QR is -7.
Did you make a sketch?
On mine I let PQ=x, then RS=x
Also let QR=y
so we have:
2x + y = 30
x + y = 23
Just subtract them and you will get y, then sub into the 2nd to get x
pretty simple.