1. 5.3 Properties of Right Triangles
CHAPTER
5.3 Properties of Right Triangles
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2. Theorem 5.13 Altitude of a Right Triangle
Theorem The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other.
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3. Writing Similarity Statements
What similarity statement can you write relating the three triangles in the diagram? Solution To help, sketch the triangles separately in the same orientation. Segment YW is the altitude to the hypotenuse of right ΔXYZ. Using Theorem There are three similar triangles. ΔXYZ ∼ ΔYWZ ∼ ΔXWY
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4. Corollary 5.14 Geometric Mean in Similar Right Triangles: Hypotenuse
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5. Corollary 5.15 Geometric Mean in Similar Right Triangles: Legs
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Theorem 5.16
The median from the right angle in a triangle is one-half the length of the hypotenuse.
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7. Using the Corollaries and Algebra
What are the values of x and y? Solution To find the altitude y, we can use Corollary 1. After that, since x is a leg of the right triangle, let’s try Corollary 2.
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8. Using the Corollaries and Algebra
What are the values of x and y? To find x.
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Finding a Distance
You are preparing for a robotics competition using the setup shown here. Points A, B, and C are located so that AB = 20 in. and Point D is located on segment AC so that and DC = 9 in. You program the robot to move from A to D and to pick up the plastic bottle at D. How far does the robot travel from A to D?
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Finding a Distance
Solution Concentrate on right ΔABC with altitude .We try Corollary 2 since we are not trying to find the altitude length BD.
Only the positive solution makes sense in this situation. The robot travels 16 in.
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