Geometry



Right Triangles Day 1

Name:_________________

Date:_____________

Warm Up

1. Let y = 5 and z = 9. Solve for x 2. Find the Geometric Mean of 8 and 25

[pic]

3. Two vehicles, each moving from a point in a straight line away from each other at an angle, are 150 feet apart after 6 seconds. Both are moving at a constant rate, vehicle A at 50 feet per second and vehicle B at 40 feet per second.

How far apart are they after 15 seconds?

[pic]

4. Line segments AC and BD intersect at E, as shown in the figure. [pic], DE = 10,

BE = 15, and CE = 20. What is the measure of [pic]?

[pic]

Pythagorean Theorem

Pythagorean Theorem –

Examples

Find the length of the unknown side of the right triangle. Determine whether the unknown side is a leg or hypotenuse.

1. 2.

3. 4.

5. A 16 foot ladder rests against the side of the house, and the base of the ladder is 4 feet away. Approximately how high above the ground is the top of the ladder?

6. Find the area of an isosceles triangle with side lengths 10 meters, 13 meters and 13 meters.

Tell whether the given triangle is a right triangle.

8. 9.

Tell whether a triangle with the given side lengths is a right triangle.

10. 4, [pic] 8 11. 10, 11, and 14 12. 5, 6, and [pic]

Classifying Triangles

c2 = a2 + b2 also written a2 + b2= c2

c2 < a2 + b2 also written a2 + b2 > c2

c2 > a2 + b2 also written a2 + b2 < c2

13. Can segments with lengths of 4.3 feet, 5.2 feet, and 6.1 feet form a triangle? If so, would the triangle be acute, right, or obtuse?

14. Show that segments with lengths 3, 4, and 6 can form a triangle and classify the triangle as acute, right, or obtuse

Geometry Name_______________________________

Worksheet – Practice Pythagorean Theorem

Find the unknown side length. Simplify answers that are radicals.

1. 2. 3.

Decide whether the numbers can represent the side lengths of a triangle. If they can, classify the triangle as right, acute, or obtuse.

4. 5, 12, 13 5. [pic]4, 6 6. 20, 21, 28

7. The length of the hypotenuse of a right triangle is 17 centimeters and the length of one leg is 15 centimeters. What is the length of the other leg?

8. The lengths of the legs of a right triangle are 3 and 5. Find the length of the hypotenuse.

9. In the right triangle QRS, [pic]RS = 13, and RQ =5. Find QS.

10. The length of the hypotenuse of a right triangle is [pic] and the length of one leg is 3. What is the length of the other leg?

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