Similarity in Right Triangles

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Presentation transcript:

Similarity in Right Triangles Geometry 8-4

Supplies One sheet of computer paper Scissors Exploration

Cut a sheet of paper into a rectangle (fold to create a perfect rectangle) Don’t be lazy and use the whole sheet of paper Exploration

Draw a diagonal on the paper, and cut Exploration

Fold and cut along the altitude of one triangle Exploration

Label the angles as shown 5 7 2 4 6 8 9 1 3 Exploration

Exploration Compare the angles on the three triangles 5 7 2 4 6 8 9 1 3 Exploration

Exploration Which angles are congruent to angle 1? 4 and 7 6 and 8 5 and 9 5 7 2 4 6 8 9 1 3 Exploration

Exploration So... What is true about all three triangles? They are similar 5 7 2 4 6 8 9 1 3 Exploration

Write a similarity statement C A B D Exploration

Geometric Mean – A proportion with the same variable in each fraction as shown Geometric Means

Example

Theorem and corollaries

Theorem and corollaries

Example

Example

Example

Example

Practice

Practice

Practice

Practice

Practice

Practice

Practice

Practice

Practice

Pages 442 – 444 15, 18, 30 – 36 even, 42, 44, 50, 52, 62 - 64 Homework