These problems were discussed last semester. In fact, they made up the content of one of your quizzes.

Problem 9

Suppose Jackie starts at point A and walks counter-clockwise around the figure. When Jackie gets to each vertex, she turns left so many degrees. Answer these questions: (1) When you take the number of "turning" degrees and add them to the angle on the inside of the polygon, what is the sum? (2) How many of the angle pairs are there around this figure? (3) What is the sum of the interior angles? (4) What is the difference of these two sums?

Problem 10

Follow the same reasoning in Problem 9. You should come to the same conclusion AND the same answer!

Problem 11

The SENTRY THEOREM says that the sum of the EXTERIOR ANGLES of polygon are always....?

Problem 12

If the hypotenuse is twice as long as the shorter leg, then by the Pythagorean Theorem, letting s be the shorter leg, the other leg must be

The perimeter of this triangle is given by the expression

Therefore, the shortest side is

Find the lengths of the remaining sides accordingly.

Problem 13

This is a SPACE DIAGONAL question. From the looks of it, I would say no.

Problem 14

Page 36

Problem 1

This problem seems to be about THREE IDEAS: (1) The SSA Criterion; (2) Using the distance formula; and (3) recognizing special right triangles.

Make sure you know where each things comes from

(a) This is all about the distance formula and using the distance formula.

(b) You can certainly use the Distance Formula again, but recognizing that this is a 45-45-90 triangle, we can deduce that the coordinates of C are (4,4).

(c) Distance formula again. I think I will just modify my Nspire document. Be careful. Angle CAB is 45 degrees, so this will limit your answer to just one of the two choices.

Problem 2

(a) In a cube, each edge has the same length. Let each edge be s. Then each diagonal has a length

(b) If I assign coordinate to the vertices of the cube, one vertex could be (0,0,0) and the opposite vertex would be (s,s,s). The midpoint of the the space diagonal between these two points is

Find the coordinates of the other six vertices, and show that their midpoints are all this point.

(c) Again, using the coordinates as in part (b), you want to select any two of the space diagonals, express them as vectors, and then show their dot product is zero.

Problem 3

The midpoint is just the average of the coordinates.

Play with this applet to get a feel for just one possible way to do this.

All the triangles are SIMILAR, just scaled copies of the original.

Problem 7

In the applet below, try your hand at typing in different combinations of u and v. Remember, the vector will start at the origin, so it wee? -MGP be PARALLEL and THE SAME LENGTH as your desired vector.

Problem 8

Problem 9

You should use the POINT TOOL below to plot the points that satisfy the conditions of the problem. Then you should derive the equation of the parabola, simplifying as much as you can, then entering the equation in the input line to see if the equation passes through your points.

Problem 10

Ahhh...a COUNTING question. If you notice in the picture below, it is possible to draw eight different right triangles that have edge EG as a side. Finish counting.

## Table of Contents

## Page 35

## Problems 1-8

These problems were discussed last semester. In fact, they made up the content of one of your quizzes.

## Problem 9

## Problem 10

Follow the same reasoning in Problem 9. You should come to the same conclusion AND the same answer!

## Problem 11

The SENTRY THEOREM says that the sum of the EXTERIOR ANGLES of polygon are always....?

## Problem 12

If the hypotenuse is twice as long as the shorter leg, then by the Pythagorean Theorem, letting

sbe the shorter leg, the other leg must beThe perimeter of this triangle is given by the expression

Therefore, the shortest side is

Find the lengths of the remaining sides accordingly.

## Problem 13

This is a

SPACE DIAGONALquestion. From the looks of it, I would say no.## Problem 14

## Page 36

## Problem 1

This problem seems to be about THREE IDEAS: (1) The SSA Criterion; (2) Using the distance formula; and (3) recognizing special right triangles.

Make sure you know where each things comes from

(a) This is all about the distance formula and using the distance formula.

(b) You can certainly use the Distance Formula again, but recognizing that this is a 45-45-90 triangle, we can deduce that the coordinates of C are (4,4).

(c) Distance formula again. I think I will just modify my Nspire document. Be careful. Angle CAB is 45 degrees, so this will limit your answer to just one of the two choices.

## Problem 2

(a) In a cube, each edge has the same length. Let each edge be

s. Then each diagonal has a length(b) If I assign coordinate to the vertices of the cube, one vertex could be (0,0,0) and the opposite vertex would be (s,s,s). The midpoint of the the space diagonal between these two points is

Find the coordinates of the other six vertices, and show that their midpoints are all this point.

(c) Again, using the coordinates as in part (b), you want to select any two of the space diagonals, express them as vectors, and then show their dot product is zero.

## Problem 3

The midpoint is just the average of the coordinates.

## Problem 4

brought to you by Livescribe

## Problem 5 and 6

Play with this applet to get a feel for just one possible way to do this.

All the triangles are SIMILAR, just scaled copies of the original.

## Problem 7

In the applet below, try your hand at typing in different combinations of

uandv. Remember, the vector will start at the origin, so it wee? -MGP be PARALLEL and THE SAME LENGTH as your desired vector.## Problem 8

## Problem 9

You should use the POINT TOOL below to plot the points that satisfy the conditions of the problem. Then you should derive the equation of the parabola, simplifying as much as you can, then entering the equation in the input line to see if the equation passes through your points.

## Problem 10

Ahhh...a COUNTING question. If you notice in the picture below, it is possible to draw eight different right triangles that have edge EG as a side. Finish counting.

## Problem 11

brought to you by Livescribe

## Problem 12

According to the SENTRY THEOREM, what do the exterior angles add up to? In a regular polygon, what is true about the exterior angles?

## Problem 13

brought to you by Livescribe

## Problem 14

Try to construct these pentagons using the rotation tool. Only one will work. Now tesselating is a different question.