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Published byKarin Rice Modified over 8 years ago
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7.1 Ratio and Proportions -Ratios: A comparison of 2 quantities -Proportion: A statement that 2 ratios are equal -Extended Proportion: When 3 or more ratios are equal -Scale Drawing: Compares the lengths in the drawing to the actual length in real life
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7.2 Similar Polygons -Similar Polygon: 1. Corresponding angles are congruent 2. Corresponding sides are proportional -Similarity Ratio: The ratio of the lengths of corresponding sides -Golden Ratio: 1.618:1 -Golden Rectangle: Can be divided into a square and a rectangle that is similar to the original rectangle
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7.3 proving Triangles are Similar -Postulate 7.1: Angle-Angle Similarity says if 2 angles of 1 triangle are congruent to 2 angles of another triangle, then the triangles are similar -Theorem 7.1: Side Side Side (SSS) Similarity says if corresponding sides of 2 triangles are proportional, then the triangles are similar -Postulate 4.2: Side Angle Side (SAS) Similarity says if an angle of 1 triangle is congruent to an angle of a 2 nd triangle, and the sides including the 2 angles are proportional, then the triangles are similar
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7.4 Similarity in right triangles -Theorem 7.3: The altitude to the hypotenuse of a right triangle divides the triangle into 2 triangles that are similar to the original triangle and to each other -Geometric Mean: For any 2 positive numbers a and b, x is the geometric mean so that so then -Corollary to Theorem 7.3: The length of the altitude to the hypotenuse of a right triangle is the geometric mean to the lengths of the segments to the hypotenuse -Corollary 2 to Theorem 7.3: The altitude to the hypotenuse of a right triangle separates the hypotenuse so that the length of each leg of the triangle is the geometric mean of the adjacent hypotenuse segment and the length of the hypotenuse
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7.5 Proportions in Triangles -Theorem 7.4: The Side-Splitter Theorem says if a line is parallel to 1 side of a triangle and intersects the other 2 sides, then it divides those sides proportionally -Corollary to Theorem 7.4: If 3 parallel lines intersect 2 transversals, then the segments intercepted on the transversals are proportional. -Theorem 7.5: The Triangle-Angle-Bisector Theorem says if a ray bisects an angle of a triangle, then it divides the opposite side into segments that are proportional to the other 2 sides of the triangle
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8.1 Pythagorean Theorem and its converse
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8.2 Special Right Triangles
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8.3 trigonometry
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8.4 Angles of elevation and depression
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