SOLUTION: triangle PQR in which QR=6cm. the line ST is parallel to QR such that PS= 3cm and SQ=5cm.
a) Prove that triangle PST is similar to triangle PQR
b) Calculate the length, in cm,
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-> SOLUTION: triangle PQR in which QR=6cm. the line ST is parallel to QR such that PS= 3cm and SQ=5cm.
a) Prove that triangle PST is similar to triangle PQR
b) Calculate the length, in cm,
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Question 872350: triangle PQR in which QR=6cm. the line ST is parallel to QR such that PS= 3cm and SQ=5cm.
a) Prove that triangle PST is similar to triangle PQR
b) Calculate the length, in cm, of ST
c) Calculate (area of triangle PST) : (area of triangle PQR)
d) Calculate (area of triangle STQ) : ( Area of triangle PQR) Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website! PQR & PST
ST||QR ( given)
angle PQR is congruent to angle PST
angle PRQ is congruent to angle PTR ( corresponding angles) seg PQ & seg PR are the transversals to parallel lines ST & QR
angle P is common angle
so triangle PQR similar to triangle PST (S-S-A) property
PS/SQ = 3/5
SQ/PS = 5/3
(PS+SQ)/PS = 8/3 ( componendo)
PQ/PS =8/3
PQ/PS = PR/PT=QR/ST = 8/3 ( ratio of sides of similar triangles)
QR/ST= 8/3
6/ST = 8/3
ST = 18/8 = 9/4= 2.25 cm
Calculate (area of triangle PST) : (area of triangle PQR)= s1^2/s2^2
=(3)^2/(8)^2
=9/64
