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Honors Geometry Section 8.5 Indirect Measurement & Additional Similarity Theorems
Similar triangles can be used to find the height of objects.
Proportional Altitudes Theorem If two triangles are similar, then corresponding altitudes are proportional to a pair of corresponding sides.
Let’s think about why this theorem is true. Assume, why is ?
Proportional Medians Theorem If two triangles are similar, then corresponding medians are proportional to a pair of corresponding sides.
Proportional Angle Bisectors Theorem If two triangles are similar, then corresponding angle bisectors are proportional to a pair of corresponding sides.
The triangles shown are similar. Solve for x.
Proportional Segments Theorem An angle bisector of a triangle divides the opposite side into segments which are proportional to the remaining two sides.
Solve for y.
Honors Geometry Section 8.6 Proportions and Similar Triangles.
Proportional Parts of a Triangle Proportional Perimeters Theorem If two triangles are similar, then the perimeters are proportional to the measures of.
11.7 Ratios of Areas Objective: After studying this section you will be able to find ratios of areas by calculating and comparing the areas and applying.
5.1 Special Segments in Triangles Learn about Perpendicular Bisector Learn about Medians Learn about Altitude Learn about Angle Bisector.
Warm-Up What is the scale factor (or similarity ratio) of the following two triangles?
Objectives To use the side-splitter theorem. To use the triangle angle-bisector theorem.
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Entry Task Find the value of x in each figure x 4 x 6 14.
Warm-Up 1 In the diagram, DE is parallel to AC. Name a pair of similar triangles and explain why they are similar.
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Notes 7.4 Parallel Lines and Proportional Parts. Review Corresponding sides of similar triangles are _____________ Corresponding angles of similar triangles.
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1 Similar Triangles Section Two polygons are similar if and only if their corresponding angles are congruent and the measures of their corresponding.
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Introduction Our project covers sections 8.4, 8.5, and 8.6. These sections discuss the side splitting theorem, indirect measurement and additional similarity.
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6.6 – Use Proportionality Theorems. Triangle Proportionality Theorem If a line parallel to one side of a triangle intersects the other two sides, then.
9.1 Similar Right Triangles Geometry. Objectives Solve problems involving similar right triangles formed by the altitude drawn to the hypotenuse of.
5-2 Median & Altitudes of Triangles The student will be able to: 1. Identify and use medians in triangles. 2. Identify and use altitudes in triangles.
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Chapter 8 mini unit. Learning Target I can use proportions to find missing values of similar triangles.
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Sec: 6.5 Sol: If two triangles are similar, then the _____________ are proportional to the measures of corresponding sides. Remember: The perimeter.
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