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.

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Presentation transcript:

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

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

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

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

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

8.1 Pythagorean Theorem and its converse

8.2 Special Right Triangles

8.3 trigonometry

8.4 Angles of elevation and depression

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