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Algebra 1 Interactive Chalkboard
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3. Lesson 11-4 The Pythagorean Theorem Lesson 11-5 The Distance Formula
Contents

4. Example 1 Find the Length of the Hypotenuse
Example 2 Find the Length of a Side
Example 3 Pythagorean Triples
Example 4 Check for Right Triangles
Lesson 4 Contents

5. Find the length of the hypotenuse of a right triangle if and
Pythagorean Theorem
and
Simplify.
Take the square root of each side.
Use the positive value.
Answer: The length of the hypotenuse is 30 units.
Example 4-1a

6. Find the length of the hypotenuse of a right triangle if and
Answer: 65 units
Example 4-1b

7. Find the length of the missing side.
In the triangle, and units.
Pythagorean Theorem
and
Evaluate squares.
Subtract 81 from each side.
Use a calculator to evaluate .
Use the positive value.
Answer: To the nearest hundredth, the length of the leg is units.
Example 4-2a

8. Find the length of the missing side.
Answer: about units
Example 4-2b

9. Multiple-Choice Test Item What is the area of triangle XYZ?
A 94 units2 B 128 units2 C 294 units2 D 588 units2
Read the Test Item
The area of the triangle is In a right triangle,
the legs form the base and height of the triangle. Use
the measures of the hypotenuse and the base to
find the height of the triangle.
Example 4-3a

10. The height of the triangle is 21 units.
Solve the Test Item
Step 1 Check to see if the measurements of this triangle are a multiple of a common Pythagorean triple. The hypotenuse is units and the leg is units. This triangle is a multiple of a (3, 4, 5) triangle.
The height of the triangle is 21 units.
Example 4-3a

11. Step 2 Find the area of the triangle.
Area of a triangle
and
Simplify.
Answer: The area of the triangle is 294 square units. Choice C is correct.
Example 4-3a

12. Multiple-Choice Test Item What is the area of triangle RST?
A 764 units2 B 480 units2 C 420 units2 D 384 units2
Answer: D
Example 4-3b

13. Answer: Since , the triangle is not a right triangle.
Determine whether the side measures of 7, 12, 15 form a right triangle.
Since the measure of the longest side is 15, let , and Then determine whether
Pythagorean Theorem
and
Multiply.
Add.
Answer: Since , the triangle is not a right triangle.
Example 4-4a

14. Answer: Since the triangle is a right triangle.
Determine whether the side measures of 27, 36, 45 form a right triangle.
Since the measure of the longest side is 45, let and Then determine whether
Pythagorean Theorem
and
Multiply.
Add.
Answer: Since the triangle is a right triangle.
Example 4-4b

15. Determine whether the following side measures form right triangles.
b. 12, 22, 40
Answer: right triangle
Answer: not a right triangle
Example 4-4b

16. End of Lesson 4

17. Example 1 Distance Between Two Points
Example 2 Use the Distance Formula
Example 3 Find a Missing Coordinate
Lesson 5 Contents

18. Find the distance between the points at (1, 2) and (–3, 0).
Distance Formula
and
Simplify.
Evaluate squares and simplify.
Answer: or about 4.47 units
Example 5-1a

19. Find the distance between the points at (5, 4) and (0, –2).
Answer:
Example 5-1b

20. Biathlon Julianne is sighting her rifle for an upcoming biathlon competition. Her first shot is 2 inches to the right and 7 inches below the bull’s-eye. What is the distance between the bull’s-eye and where her first shot hit the target?
Draw a model of the situation on a coordinate grid. If the bull’s-eye is at (0, 0), then the location of the first shot is (2, –7). Use the Distance Formula.
Example 5-2a

21. Example 5-2a

22. Answer: The distance is or about 7.28 inches.
Distance Formula
and
Simplify.
or about 7.28 inches
Answer: The distance is or about 7.28 inches.
Example 5-2a

23. Horseshoes Marcy is pitching a horseshoe in her local park
Horseshoes Marcy is pitching a horseshoe in her local park. Her first pitch is 9 inches to the left and 3 inches below the pin. What is the distance between the horseshoe and the pin?
Answer:
Example 5-2b

24. Find the value of a if the distance between the points at (2, –1) and (a, –4) is 5 units.
Distance Formula
Let
and .
Simplify.
Evaluate squares.
Simplify.
Example 5-3a

25. Subtract 25 from each side.
Square each side.
Subtract 25 from each side.
Factor.
Zero Product Property or
Solve.
Answer: The value of a is –2 or 6.
Example 5-3a

26. Find the value of a if the distance between the points at (2, 3) and (a, 2) is
Answer: –4 or 8
Example 5-3b

27. End of Lesson 5

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34. End of Slide Show