Warm up: The diagram below includes two squares: one has sides of length 20 and the other has sides of length 10. What is the area of the shaded region?

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Presentation transcript:

Warm up: The diagram below includes two squares: one has sides of length 20 and the other has sides of length 10. What is the area of the shaded region? Area of shaded region = 100

Similarity Proofs HMWK Answers 1)

Similarity Proofs HMWK Answers 2)

Similarity Proofs HMWK Answers 3)

Similarity Proofs HMWK Answers 4)

Similarity Proofs HMWK Answers 5)

Similarity Proofs HMWK Answers 6)

Hands on… 1)Get a pink ½ sheet of paper from the front. 2)Draw a line from 1 vertex to the opposite vertex. 3)Draw another line from either of the non-connected vertices perpendicular to the 1 st line drawn. 4)Cut out the 3 triangles and align them as shown. What do you notice about the triangles?

We just demonstrated the following important theorem about right triangles… Right Triangle Altitude Theorem In a rt. ∆, the altitude from the vertex of the right angle to the hypotenuse forms 2 ∆’s that are similar to the given ∆ and to each other.

Given Definition of altitude Definition of perpendicular Definition of right angle Definition of congruent angles Reflexive Prop. of Congruence AA Similarity Thm. Transitive Prop.

Geometric Means Theorems

Find x, y, and z. X = 144 Y = 60 Z = 156

Find x, y, and z.

The segments of the hypotenuse measure 4 inches and 16 inches.