(6) Find the highest angle of rhombus PQRS
in which altitude from p to Rs bisects Rs=
Answers
Highest angle of rhombus PQRS = 120° in which altitude from P to side RS bisects RS
Step-by-step explanation:
Let say PM ⊥ RS bisects RS
=> RM = SM = RS/2
PQRS is rhombus
=> PQ = QR = RS = PS
Comparing Δ PMS & Δ PMR
PM = PM (common)
SM = RM
∠PMS = ∠PMR = 90°
=> Δ PMS ≅ Δ PMR
=> PS = PR
=> PQ = QR = PR = RS = PS
Hence ΔPQR & ΔPRS are Equilateral Triangle
=> ∠PQR = ∠PSR = 60°
∠QPS = ∠QPR + ∠QPS = 60° + 60° = 120°
∠QRS = ∠QRP + ∠SRP = 60° + 60° = 120°
Highest angle of rhombus PQRS = 120° in which altitude from P to side RS bisects RS
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