Suppose KLMN is a parallelogram, and that the bisectors of ∠K and ∠L meet at A. Prove that A is equidistant from LM and KN.
1 answer:
Answer:
This is proved by ASA congruent rule.
Step-by-step explanation:
Given KLMN is a parallelogram, and that the bisectors of ∠K and ∠L meet at A. we have to prove that A is equidistant from LM and KN i.e we have to prove that AP=AQ
we know that the diagonals of parallelogram bisect each other therefore the the bisectors of ∠K and ∠L must be the diagonals.
In ΔAPN and ΔAQL
∠PNA=∠ALQ (∵alternate angles)
AN=AL (∵diagonals of parallelogram bisect each other)
∠PAN=∠LAQ (∵vertically opposite angles)
∴ By ASA rule ΔAPN ≅ ΔAQL
Hence, by CPCT i.e Corresponding parts of congruent triangles PA=AQ
Hence, A is equidistant from LM and KN.
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Answer: The answer is 0 hours and 10 hours.
Step-by-step explanation: Given that me and my friend are on a road trip. My speed is 70 miles per hour and my friend's speed is 60 miles per hour. Our plan is to drive less than 15 hours and at least 600 miles each day.
Also, my friend will drive more hours than me.
Let, 'x' and 'y' be the number of hours drove by me and my friend respectively. Then, according to the given information, we have the following inequalities.
When we plot these inequalities in a graph paper, we can see in the attached figure, where the common shaded region gives the solution set, one of the solution is point 'P', given by
x = 0 and y = 10.
This solution satisfy all the three conditions given above.
Thus, one of the solution is - I will drive for 0 hours and my friend will drive for 10 hours.
