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Proportions in Triangles

Proportions in Triangles. Side-Splitter Theorem Theorem 7-4: Side-Splitter Theorem: If a line is parallel to one side of a triangle and intersects the

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Page 1: Proportions in Triangles. Side-Splitter Theorem Theorem 7-4: Side-Splitter Theorem: If a line is parallel to one side of a triangle and intersects the

Proportions in Triangles

Page 2: Proportions in Triangles. Side-Splitter Theorem Theorem 7-4: Side-Splitter Theorem: If a line is parallel to one side of a triangle and intersects the

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

Page 3: Proportions in Triangles. Side-Splitter Theorem Theorem 7-4: Side-Splitter Theorem: If a line is parallel to one side of a triangle and intersects the

Side-Splitter Proof

Statements Reasons

1.

2.

3.

4.

5.

6.

7.

1.

2.

3.

4.

5.

6.

7.

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

Page 4: Proportions in Triangles. Side-Splitter Theorem Theorem 7-4: Side-Splitter Theorem: If a line is parallel to one side of a triangle and intersects the

Side-Splitter Theorem

Find the value of x.

Find the value of x.

Page 5: Proportions in Triangles. Side-Splitter Theorem Theorem 7-4: Side-Splitter Theorem: If a line is parallel to one side of a triangle and intersects the

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

Page 6: Proportions in Triangles. Side-Splitter Theorem Theorem 7-4: Side-Splitter Theorem: If a line is parallel to one side of a triangle and intersects the

ApplicationGiven that the edges of the panels of the sails are parallel, find the values of the variables.

Page 7: Proportions in Triangles. Side-Splitter Theorem Theorem 7-4: Side-Splitter Theorem: If a line is parallel to one side of a triangle and intersects the

You wanna try one? Too bad! ;)Find the values of the variables in the following figure.

Page 8: Proportions in Triangles. Side-Splitter Theorem Theorem 7-4: Side-Splitter Theorem: If a line is parallel to one side of a triangle and intersects the

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.

Page 9: Proportions in Triangles. Side-Splitter Theorem Theorem 7-4: Side-Splitter Theorem: If a line is parallel to one side of a triangle and intersects the

Triangle-Angle-Bisector TheoremFind the value of x in the following figure.

Find the value of x in the following figure.

Page 10: Proportions in Triangles. Side-Splitter Theorem Theorem 7-4: Side-Splitter Theorem: If a line is parallel to one side of a triangle and intersects the

Kick it up a notch!!!

Find the value of x.

Page 11: Proportions in Triangles. Side-Splitter Theorem Theorem 7-4: Side-Splitter Theorem: If a line is parallel to one side of a triangle and intersects the

Kick it up a notch!!!

Find the value of x.

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