“Is it better to be feared or respected? And I say, is it too much to ask for both?”

7.5: Proportions in Triangles

LT: I will use the Side-Splitter Thm. and the Triangle Bisector Thm.

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.

Side-Splitter Theorem

Find the value of x.

Find the value of x.

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.

You wanna try one? Find the values of the variables in the following figure.

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.

“Don’t worry Wilson, I’ll do all the paddling. You just hang on!”

7.5 Proportions in Triangles

HW 7.5: #1-7, 8-24 even, 25, 27, 31-33

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

Kick it up a notch!!!

Find the value of x.

Kick it up a notch!!!

Find the value of x.