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worty [1.4K]
2 years ago
9

Complete the two-column proof by providing a reason for each of the five statements.

Mathematics
1 answer:
koban [17]2 years ago
7 0

I will only be writing the reasons for each and you can respond if you need clarification for anything:

1. given

2. opposite sides of a parallelogram are congruent (and a rectangle is a parallelogram so the properties apply)

3. def rectangle

4. SAS (side angle side congruence theorem)

5. CPCTC (congruent parts of congruent triangles are congruent)

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<h3>Answer: Approximately 6.4 units</h3>

==================================================

Explanation:

The origin is the point (0,0)

Use the distance formula to find the distance from (0, 0) to (4, -5)

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(x_1,y_1) = (0,0)\\\\(x_2,y_2) = (4,-5)\\\\

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d = \sqrt{\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2}\\\\d = \sqrt{\left(0-4\right)^2+\left(0-(-5)\right)^2}\\\\d = \sqrt{\left(0-4\right)^2+\left(0+5\right)^2}\\\\d = \sqrt{\left(-4\right)^2+\left(5\right)^2}\\\\d = \sqrt{16+25}\\\\d = \sqrt{41} \ \text{ exact distance}\\\\d \approx 6.40312 \ \text{ approximate distance}\\\\d \approx 6.4\\\\

The distance between the two points (0,0) and (4,-5) is approximately 6.4 units.

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