Which statement proves that the diagonals of square PQRS are perpendicular bisectors of each other? The length of SP, PQ, RQ, an
2 answers:
Answer:
Step-by-step explanation:
Given is a square PQRS. Its diagonals are PR and QS.
To prove that PR is perpendicular to QS
We have been given as
SP = PQ =RQ =SR =5.
Using Pythagorean theorem we have
both diagonals will equal
If P is the origin, (say) then coordinates of vertices would be (0,0) (5,0) (5,5) and (0,5)
Mid point would be (2.5,2.5) for both
Slope of RP = change in y coordinate/change in x coordinate
= 1
Slope of QS = 5/-5 = -1
Product of the two slopes = -1
Hence the two diagonals are perpendicular
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