GEOMETRY: Chapter 99.1 Similar Right Triangles

Theorem 9.1If the altitude is drawn to the hypotenuse of a right

triangle, then the two triangles formed are similar to the original triangle and to each other.

Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 449.

Ex. 1: Identify the similar triangles in the

diagram.

Answer: tri DEF ~ triangle DGE ~ Tri EGF

Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 450.

Ex. 2:The figure below shows the side view of a tool

shed. What is the maximum height, h, of the shed?

Answer: 16.1 ft

Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 450.

Ex. 3:

Find the value of k.

Answer: 2 sq root 5Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 451.

Theorem 9.2 Geometric Mean (Altitude) Theorem

In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments.

The length of the altitude is the geometric mean of the lengths of the other two sides.

Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 452.

Theorem 9.3 Geometric Mean (Leg) Theorem

In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments.

The length of each leg of the right triangle is the geometric mean of the lengths of the hypotenuse that is adjacent to the leg.

Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 452.

Ex. 4:You are standing by a tree as shown in the diagram. A 25 foot ladder is leaning against the tree. What is the length of a piece of rope that goes from the base of the tree and is perpendicular to the ladder?

Answer: 4.9 ftImages taken from: Geometry. McDougal Littell: Boston, 2007. P. 452.

9.1, p. 531, #1-29 odds

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