LN is point on side QR of triangle PQR. If LM is parallel to PR and LN is parallel to PQ and a line MN meets the produced line QR at T as given in the figure, then prove that LT^2 = RT × TQ
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In triangle QRT
LM parallel to PR
Therefore by BPT,
TN/TM =RT/TL ---------Eq 1
in triangle QRT
LN parallel to PQ
since M lies on PQ
LN is parallel to MQ
therefore
LT/QT = TN/TM ---------- Eq 2
from eq1 and eq2
RT/TL=LT/QT
rearranging
RT/LT=LT/TQ
THEREFORE
LT^2=RT x TQ
LM parallel to PR
Therefore by BPT,
TN/TM =RT/TL ---------Eq 1
in triangle QRT
LN parallel to PQ
since M lies on PQ
LN is parallel to MQ
therefore
LT/QT = TN/TM ---------- Eq 2
from eq1 and eq2
RT/TL=LT/QT
rearranging
RT/LT=LT/TQ
THEREFORE
LT^2=RT x TQ
Answered by
0
Answer:
given : LM ll PR
LN ll PQ
Step-by-step explanation:
in triangle qtm L N S PARALLEL TO MQ FROM BPT we can say that TL upon lq TN UPON TN UPON MN
QTM LMS PARALLEL TO NR FROM BBT WE CAN PROVE THAT TR UPON RQ TN UPON MN FROM ONE AND TWO WE CAN SHOW THAT LT SQUARE IS EQUAL TO RT INTO QT
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