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