Mathematics
In parallelogram PQRS, L is mid-point of side SR and SN is drawn parallel to LQ which meets RQ produced at N and cuts side PQ at M. Given, RN = 25 cm calculate the length of SP.
Mid-point Theorem
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Answer
12.5 cm
Reason
In △ SRN :
L is mid-point of SR and LQ // SN [Given]
∴ LQ bisects RN [Line through mid-point of one side of a △ and parallel to another side bisects the third side]
i.e., RQ = QN = RN
⇒ RQ = RN
We know that,
Opposite sides of a parallelogram are equal.
∴ SP = = 12.5 cm
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Related Questions
ABC is a triangle right angled at C and M is mid-point of hypotenuse AB. Line drawn through M and parallel to BC intersects AC at D. Show that :
(i) D is mid-point of AC.
(ii) MD is perpendicular to AC.
(iii) CM = MA = AB
Assertion (A): Using the information in the given figure, we get CE : EA = 5:3.
Reason (R): Since, ∠ADE = ∠ABC = 90°
so,
⇒ CE : EA = 3 : 5
- A is true, R is false.
- A is false, R is true.
- Both A and R are true.
- Both A and R are false.