Similarity in Right Triangles Geometry 8 4 Supplies

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 Exploration 3

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

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

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

• Write a similarity statement C A D Exploration B

• 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

• Pages 442 – 444 • 15, 18, 30 – 36 even, 39, 42, 44, 50, 52, 62 - 64 Honors Homework