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**Sarah Scheuer, Brian Waronker Dean Smith**

8.4 – 8.6 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 X 12x = 240; X = 20 12 15 > 16 X >

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**Important Things To Know**

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

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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.歳汣耀ǨRatios 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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The product of the means equals the product of the extremes.

The product of the means equals the product of the extremes.

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