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8.4 – 8.6 Sarah Scheuer, Brian Waronker Dean Smith Sarah Scheuer, Brian Waronker Dean Smith

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Introduction to 8.4 Side-Splitting Theorem – A line parallel to one side of the triangle divides the other two sides proportionally.

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Practice 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 1215 X > >

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Important Things To Know Two-Transversal Proportionality Corollary – Three or more parallel lines divide two intersecting transversals proportionally. A B C W X Y

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8.5 Indirect 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 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. Ǩ Ratios 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. Ǩ Ratios O

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Practice 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?

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PRACTICE QUIZ Find x

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

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websites http://summit.k12.co.us/schools/Shs/StaffW ebPages/YankowsK/IB4/IBMath4Ch8.htm http://www.mathleague.com/help/geome try/geometry.htm http://summit.k12.co.us/schools/Shs/StaffW ebPages/YankowsK/IB4/IBMath4Ch8.htm http://summit.k12.co.us/schools/Shs/StaffW ebPages/YankowsK/IB4/IBMath4Ch8.htm http://www.mathleague.com/help/geome try/geometry.htm http://summit.k12.co.us/schools/Shs/StaffW ebPages/YankowsK/IB4/IBMath4Ch8.htm http://www.mathleague.com/help/geometry/geometry.htmhttp://www.mathleague.com/help/geometry/geometry.htm

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