Section 9.1 Similar Right Triangles
OBJECTIVE:• To find and use relationships in similar right triangles
BIG IDEAS:• REASONING AND PROOF
• VISUALIZATION PROPORTIONALITYESSENTIAL 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.
ABC ACD
ABC CBD
ACD CBD
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
AD CD
CD DB
AB AC AB CB
AC AD CB DB
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. 53111 – 15 all, 16 – 32 evens, 23, 29, 31; 41, 42, 45 – 51x3
22 questions
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