8.4 – 8.6 8.4 – 8.6

Sarah Scheuer,

Brian Waronker

Dean Smith

Sarah Scheuer,

Brian Waronker

Dean Smith

Introduction to 8.4Introduction to 8.4 Side-Splitting Theorem – A line parallel to

one side of the triangle divides the other two sides proportionally.

Side-Splitting Theorem – A line parallel to one side of the triangle divides the other two sides proportionally.

upper left upper right

lower left lower right=

upper left lower left

upper right lower right=

upper left upper right

whole left whole right=

lower left lower right

whole left whole right=

Practice QuestionPractice Question

Solve for X using the side splitting theorem.

ANSWER: 12 = 15

16 X 12x = 240; X = 20

Solve for X using the side splitting theorem.

ANSWER: 12 = 15

16 X 12x = 240; X = 20

16

12 15

X

>

>

Important Things To KnowImportant Things To Know

Two-Transversal Proportionality Corollary – Three or more parallel lines divide two intersecting transversals proportionally.

Two-Transversal Proportionality Corollary – Three or more parallel lines divide two intersecting transversals proportionally.

A

B

C

W

X

Y

8.5Indirect Measurement and Additional

Similarity Theorems

8.5Indirect Measurement and Additional

Similarity Theorems Proportional Altitude Theorem- If two triangles are

similar, then their corresponding altitudes have the same ratio as their corresponding sides

Proportional Medians Theorem- if two triangles are similar, then their corresponding medians have the same ratio as their corresponding sides

Proportional Angle Bisectors Theorem- if two triangles are similar, then their corresponding angle bisectors have the same ratio as the corresponding sides

Proportional Segments Theorem- an angle bisector of a triangle divides the opposite side into two segments that have the same ratio as the other two sides

Proportional Altitude Theorem- If two triangles are similar, then their corresponding altitudes have the same ratio as their corresponding sides

Proportional Medians Theorem- if two triangles are similar, then their corresponding medians have the same ratio as their corresponding sides

Proportional Angle Bisectors Theorem- if two triangles are similar, then their corresponding angle bisectors have the same ratio as the corresponding sides

Proportional Segments Theorem- an angle bisector of a triangle divides the opposite side into two segments that have the same ratio as the other two sides

8.6 Area And Volume Ratios8.6 Area And Volume Ratios

Ratios Of Areas of similar Figures Side of square A and side of square B = 3/1 Area of square A and area of Square B = (3/1) squared. Ratios Of Volumes Edge of cube A and edge of cube B = 3/1 Volume of cube A and volume of cube B = (3/1) cubed. 歳汣耀

ǨRatios O

Ratios Of Areas of similar Figures Side of square A and side of square B = 3/1 Area of square A and area of Square B = (3/1) squared. Ratios Of Volumes Edge of cube A and edge of cube B = 3/1 Volume of cube A and volume of cube B = (3/1) cubed. 歳汣耀

ǨRatios O

Practice QuestionsPractice Questions

The ratio of corresponding edges of two similar pyramids is 7/5. ･What is the area of their bases? ･What is their volumes?The Height of two similar cones is 7/9 ･What is their radii? ･What ist heir volumes? ･What is their area and base?

The ratio of corresponding edges of two similar pyramids is 7/5. ･What is the area of their bases? ･What is their volumes?The Height of two similar cones is 7/9 ･What is their radii? ･What ist heir volumes? ･What is their area and base?

PRACTICE QUIZPRACTICE QUIZ

Find x Find x

Quiz continuedQuiz continued

The ratio of the sides of two similar triangles is 1/3. What is the ratio of their areas????

The ratio of the sides of two similar triangles is 1/3. What is the ratio of their areas????

websiteswebsites

http://summit.k12.co.us/schools/Shs/StaffWebPages/YankowsK/IB4/IBMath4Ch8.htm http://www.mathleague.com/help/geometry/geometry.htm

http://summit.k12.co.us/schools/Shs/StaffWebPages/YankowsK/IB4/IBMath4Ch8.htm http://www.mathleague.com/help/geometry/geometry.htm