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Please help!!! I need this and I also don't understand ​​

Please help!!! I need this and I also don't understand ​​-example-1
User Cuado
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1 Answer

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14 votes

Answer:

Explanation:

(i)

PQRS is a parallelogram (given)

∴ QT = TS (Diagonals of a parallelogram bisects each other)

also, QT = RM (given)

∴TS = RM

PQRS is a parallelogram,

∴RT = PT (Diagonals of a parallelogram bisects each other)

also, SM = PT (given)

∴RT = SM

TS = RM

RT = SM

∴ RTSM is a parallelogram (both pairs of opposite sides are equal in length)

(ii)

QP // RS (Opposite sides of a parallelogram are parallel)

∴ ∡RQP = ∡NRS (Corresponding ∡s)

RTSM is a parallelogram(Proved above)

∴MS // RT (Opposite sides of a parallelogram are parallel)

∴NS//RP

∴∡RNS = ∡ QRP (Corresponding ∡s)

in ΔPQR and Δ NSR,

QP = RS (Opposite sides of a parallelogram are equal)

∡RQP = ∡NRS (Proved above)

∡RNS = ∡ QRP(Proved above)

∴ ΔPQR≡ΔSRN (AAS)

Corresponding sides of ≡ Δs are equal, ∴QR = RN

User Sizuji
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