Section 9.1 Similar Right Triangles OBJECTIVE: To find and use relationships in similar right triangles BIG IDEAS: REASONING AND PROOF VISUALIZATIONPROPORTIONALITY ESSENTIAL UNDERSTANDINGS: Drawing in the altitude to the hypotenuse of a right triangle forms three pairs of similar right triangles The altitude to the hypotenuse of a right triangle, the segments formed by the altitude, and the sides of the right triangle have lengths that are related using the geometric means. MATHEMATICAL PRACTICE: Make sense of problems and persevere in solving them

Similar triangles Similar triangles are created when the altitude of a right triangle is drawn to the hypotenuse. The segments created in and existing in these triangles are related to the concept of geometric mean. THEOREM 9.1 If the ____________________ to the ____________________ of a right triangle divides the triangle into two triangles that are ____________________ to the original triangle and to each other.

EX 1: The diagram shows the approximate dimensions of a right triangle A)Identify the similar triangles in the diagram B)Find the height h of the triangle

Theorems 9.2 and 9.3 THEOREM 9.2: The length of the ____________________ to the hypotenuse of a right triangle is the ____________________ mean of the lengths of the segments of the ____________________ THEOREM 9.3: The ____________________ to the hypotenuse of a right triangle separates the hypotenuse so that the length of each __________ of the triangle is the geometric mean of the length of____________________ and the length of the segment of the hypotenuse ____________________ to the leg

EX 2: Find the value of the variable A)

EX 2: Find the value of each variable B)

EX 2: Find the value of each variable C)

9.1 p – 15 all, 16 – 32 evens, 23, 29, 31; 41, 42, 45 – 51x3 22 questions