Complete Problem #28 in Section 1.5 Exercises (Chapter 1) of Essentials of Geometry for College Students. Use the table below to show your work and solve the problem. You may add or delete rows as necessary.
Statements Reasons
PQ=RS Given
PS=PQ+RS Segment Addition Postulate
PR=QS Substitution Law
The problem is....
PQ = RS. Prove PR = QS.
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P Q R S
To prove PR = QS, we can use the given information that PQ = RS and the segment addition postulate.
First, substitute PQ + RS for PS using the segment addition postulate. This is valid because it states that if points P, Q, R are collinear, then any point Q between P and R can be expressed as PQ + QR.
So, we have PS = PQ + RS.
Next, we can use the substitution law to show that PR = QS. The substitution law states that if a quantity A is equal to a quantity B, then B can be substituted for A in any expression.
In this case, we can substitute PS for PQ + RS, which gives us PR = PQ + RS.
Since we know PQ = RS from the given information, we can substitute PQ for RS in the expression PR = PQ + RS.
This gives us PR = PQ + PQ.
And since PQ + PQ is equal to twice PQ, we can simplify the expression to PR = 2PQ.
Finally, we can observe that QS is also equal to 2PQ, because RS = PQ and PS = PQ + RS.
Therefore, PR = QS.
To complete the table:
P Q R S
PQ RS PR = 2PQ QS = 2PQ
Remember to show your work and explain each step clearly in the table.