Chapter 4.3, Problem 12E

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6th Edition

Daniel C. Alexander + 1 other

ISBN: 9781285195698

Textbook Problem

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*In Exercises 11 to 14, consider*
*MNPQ* with diagonals
*When the answer is not a whole number, leave a square root answer.*

*Exercises 11 â€“ 14*

If *QP = 9* and *NP* = 6, find *NQ* and *MP.*

To determine

**To find:**

*NQ* and *MP* of the given rectangle.

Explanation

**The basic property of rectangle:**

1) All the properties of a parallelogram apply (the ones that matter here are parallel sides, opposite sides are congruent, and diagonals bisect each other).

2) All angles are right angles by definition.

3) The diagonals are congruent.

**Calculation:**

Given: *QP = 9* and *NP* = 6

Consider the rectangle.

To find *NQ* and *MP*:

From the property, opposite sides are congruent in rectangle.

So, *MN* = *QP* = 9

*MQ* = *NP* = 6

Let us take right

By using Pythagorean Theorem

Let us take right

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