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Geometry

Worksheet 7.2 – Converse of the Pythagorean Theorem

1. Write the Pythagorean Theorem Extension of the Pythagorean Theorem

2. If the triangle is acute then c2 ____ a2 + b2

3. If the triangle is obtuse then c2 _____ a2 + b2

Are the triangles below right triangles? If not, what kind of triangles are they? 4. 5. 6. Determine whether the numbers can represent the side lengths of a triangle. (Recall that any two side lengths must sum to more than the third to form a triangle) If they can, classify the triangle as acute, right, or obtuse. Show work! 7. 26, 35, 62 8. 29, 18, 14 9. 30, 78, 72 10. 17, 19, 22 Find the perimeter of each figure. (answers rounded to nearest hundredth) 11. 12. Perimeter = _______ Perimeter = _______

20 in

11 in

14 in

20 m

10 m 16 m

9 15

12

15

36

4 95

7

8

113

Name ________________

13. As part of your exercise routine you jog around a park which is shaped like a right isosceles triangle. One side of the park, the hypotenuse of the triangle, is 850 feet long.

a. What are the lengths of the other two sides that create the park?

b. The recreation board would like to place a fence around the perimeter of the park. The cost of the fencing is $3.00 per foot. How much money will it cost to fence in the park?

c. The recreation board also wants to plant new grass over the entire park. How many square feet will need to be covered with grass seed?

14. Mr. Winston is adding a sunroom to his house. After laying the foundation and building the frame he double checks his measurements. Mr. Winston found that his 14 ft by 13 ft (rectangular) sunroom had a diagonal measurement of 20 ft. Why is Mr. Winston in trouble?