 Lesson 7-4.  Draw one of the diagonals for your rectangle to form two right triangles. Q: What is the relationship between the two right triangles?

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Presentation transcript:

 Lesson 7-4

 Draw one of the diagonals for your rectangle to form two right triangles. Q: What is the relationship between the two right triangles? How do you know?  In one triangle, draw the altitude from the right angle to the hypotenuse. Q: What tools/methods can you use to draw the altitude?

 Number the angles as shown. Then cut out the three triangles.  Are any of the triangles similar? Explain how you know?

 If the altitude is drawn from the right angle to the hypotenuse in a right triangle, then the two smaller triangles formed are similar to each other and to the original triangle.

 Find the geometric mean between 4 and 18.

 The length of the altitude to the hypotenuse of a right triangle is the geometric mean between the lengths of the two segments of the hypotenuse.

 Consider the three triangles formed by the altitude drawn to the hypotenuse of a right triangle.  Write a proportion relating the corresponding sides of the smallest triangle to the original (largest) triangle.  Write a proportion relating the corresponding sides of the “middle” triangle to the original triangle.

 This one is REALLY hard to write in a concise way, so it’s very WORDY!  The altitude to the hypotenuse of a right triangle divides the hypotenuse into two segments such that each leg of the triangle is the geometric mean between the length of the entire hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.

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