I Need help doing a geometry proof.
In the figure below, PQ=RS. Prove PR=QS.
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P Q R S
PR+RS = PS
PQ+QS = PS
so,
PR+RS = PQ+QS
but, PQ=RS, so
PR + PQ = PQ + QS
so,
PR = QS
To prove that PR=QS, we will use the fact that PQ=RS. Here's how we can approach the geometry proof:
Step 1: Given the figure with PQ=RS.
Step 2: Draw segment PR and segment QS to connect the opposite vertices.
Step 3: Since PQ=RS, we can say that segment PQ is congruent to segment RS, which can be written as PQ ≅ RS.
Step 4: By the definition of congruence, we know that if two segments are congruent, then their corresponding parts (endpoints) are also congruent. Therefore, we can say that point P and point R are congruent, which can be written as P ≅ R. Similarly, we can say Q ≅ S.
Step 5: By using the reflexive property of congruence, we know that any segment is congruent to itself. Therefore, we can say that PR ≅ PR and QS ≅ QS.
Step 6: By the transitive property of equality, if two segments are congruent to a common segment, then they are congruent to each other. Therefore, since PR ≅ PR and PQ ≅ RS, we can conclude that PR ≅ QS.
Step 7: Reread the proof, checking for any unclear statements or gaps in the reasoning.
Step 8: Write the conclusion of the proof: PR=QS.
Remember to state the given information, use relevant definitions and properties, and clearly explain each step you take.