Post on 30-Dec-2015
transcript
Side-Splitter Theorem
Theorem 7-4: Side-Splitter Theorem: If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally.
SY
QS
RX
QR
QS
SY
QR
RX
Side-Splitter Proof
Statements Reasons
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7.
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RS || XY
Given : QXY with RS || XY
Prove : XRRQ
YSSQ
13,2 4
QXY ~ QRS
XQ
RQYQ
SQ
XQXR RQ,YQYS SQ
XR RQRQ
YS SQSQ
XR
RQYS
SQ
Corollary to Side-Splitter Theorem
Corollary to Theorem 7-4: If three parallel lines intersect two transversals, then the segments intercepted on the transversals are proportional.
a
bc
d
ApplicationGiven that the edges of the panels of the sails are parallel, find the values of the variables.
Triangle-Angle-Bisector Theorem
Triangle-Angle-Bisector Theorem: If a ray bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the other two sides of the triangle.
Triangle-Angle-Bisector TheoremFind the value of x in the following figure.
Find the value of x in the following figure.