In a quadrilateral ABCD BM and DN are drawn perpendicular to AC such that BM=DN.show that DRN is congruent to BMR if Br=8,find BD
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Answer:
ΔBMR ≅ ΔDRN
BD = 16
Step-by-step explanation:
in ΔBMR & ΔDRN
∠BMR = ∠DNR = 90°
∠MRB = ∠NRD ( opposite angles)
if two angles of a triangle are equal then third angle will also be equal
as sum of three angles = 180°
∠MBR = ∠NDR
so
ΔBMR ≅ ΔDRN
BM/DN = BR/DR = MR/RN
BM = DN => BM/DN = 1
=> 1 = BR/DR
=> DR = BR
=> DR = 8
BD = BR + DR
=> BD = 8 + 8 = 16
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