8.4 – 8.6 sarah scheuer, brian waronker dean smith sarah scheuer, brian waronker dean smith
TRANSCRIPT
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8.4 – 8.6 8.4 – 8.6
Sarah Scheuer,
Brian Waronker
Dean Smith
Sarah Scheuer,
Brian Waronker
Dean Smith
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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=
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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
>
>
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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
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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
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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
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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?
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PRACTICE QUIZPRACTICE QUIZ
Find x Find x
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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????
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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