Two proofs that the angles in a quadrilateral sum to 360 degrees are found in the pictures below. You should be certain that you understand BOTH proofs. Then you should answer the remaining questions, which have answers 540, 720, and 9900 respectively.

Problem 3

Problem 4

n=33, w=108, u=26

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

(a) If point P is on the line y=x, then point P is equidistant from the coordinate axes.

QUESTION: Are both the statement and its converse true? Not true? Can't determine?

(b) If x=1, then x^2=1

Converse: If x^2=1, then x=1

(c) If x=1, then x^3=1.

Converse: If x^3=1, then x=1.

Problem 10

Converse: If a quadrilateral has both pairs of opposite angles congruent, then the quadrilateral is a parallelogram.

This is TRUE!

Problem 11

Look back at problem 7 above. Then try to find other ways to do it.

If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

This is true.

Problem 5

Problem 6

Problem 7

Some basic angle chasing...

Problem 8

First off, you must calculate the length. If you have done that correctly, the length is

Next, find any other vector such that the dot product with it and [6,2,3] is zero. I choose the vector [3,0,-6]. To make it the same length as the given vector, I divide by its length, and multiply by 7.

## Table of Contents

## Page 33

## Problem 1

## Problem 2

Two proofs that the angles in a quadrilateral sum to 360 degrees are found in the pictures below. You should be certain that you understand BOTH proofs. Then you should answer the remaining questions, which have answers 540, 720, and 9900 respectively.

## Problem 3

## Problem 4

n=33, w=108, u=26

## Problem 5

## Problem 6

## Problem 7

## Problem 8

## Problem 9

(a) If point P is on the line

y=x, then point P is equidistant from the coordinate axes.QUESTION:Are both the statement and its converse true? Not true? Can't determine?(b) If x=1, then x^2=1

Converse: If x^2=1, then x=1

(c) If x=1, then x^3=1.

Converse: If x^3=1, then x=1.

## Problem 10

Converse: If a quadrilateral has both pairs of opposite angles congruent, then the quadrilateral is a parallelogram.

This is TRUE!

## Problem 11

Look back at problem 7 above. Then try to find other ways to do it.

## Page 34

## Problem 1

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## Problem 2

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## Problem 3

## Problem 4

If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

This is true.

## Problem 5

## Problem 6

## Problem 7

Some basic angle chasing...

## Problem 8

First off, you must calculate the length. If you have done that correctly, the length is

Next, find any other vector such that the dot product with it and [6,2,3] is zero. I choose the vector [3,0,-6]. To make it the same length as the given vector, I divide by its length, and multiply by 7.

Now, multiply by 7.

## Problem 9

## Problem 10

## Problem 11 and 12

## Problem 13

## Problem 14

to be discussed in class.

## Problem 15

Well? In what sense is a transformation a function??