Here is a lego model of the beautiful building Fallingwater. The original was designed in 1935 by Frank Lloyd Wright. This took me about 5 hours and consists of 811 pieces.

Example Problem:

Two different points on the line y=2 are each exactly 13 units from the point (7,14). Draw a picture of this situation, and then find the coordinates of these points.

For this equation, I drew a line straight down from the point (7,14)- which is point B on the diagram, that intersected the line y=2. This forms one side of a triangle with the point your trying to find being the other. Since the point is supposed to be 13 units away from point B, you now know the length of 2 sides of the triangle, C and D. To find the base length of the triangle use the pythagorean theorem.

So, you're first point is 5 units away from point D and the second is -5 units from point D. These points are (2,2) and (12,2).

Here is a simple applet illustrating the relationship between perpendicular lines.

Triangle Constructions:

Sequence Applet:

Transformation Applet:

Screen cast construction with Geogebra 3D

Winter Break Challenge

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vectors

Parallelogram from Midpoints

parallelogram 1

Parallelogram Proofs Challenge

Page 37,problem 2 : It is given that ABCD and PBQD are parallelograms. Which of the numbered angles must be the same size as the angle numbered 1?

The angle numbers that are highlighted in red all should be the same size as angle number 1.
This can is true because when two parallel lines are cut by a transversal line, their alternate interior angles should be the same. All the high lighted angles are congruent because angle 4 is the alternate angle of 1, 7 is the alternate angle of 4, 9 is the alternate of 7, 12 is the alternate of 9, 15 is the alternate of 12, which then leads back to angle 1 being the alternate angle of 15.

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## Lily A. Portfolio Problem

Here is a lego model of the beautiful building Fallingwater. The original was designed in 1935 by Frank Lloyd Wright. This took me about 5 hours and consists of 811 pieces.

Example Problem:Two different points on the line y=2 are each exactly 13 units from the point (7,14). Draw a picture of this situation, and then find the coordinates of these points.

For this equation, I drew a line straight down from the point (7,14)- which is point B on the diagram, that intersected the line y=2. This forms one side of a triangle with the point your trying to find being the other. Since the point is supposed to be 13 units away from point B, you now know the length of 2 sides of the triangle, C and D. To find the base length of the triangle use the pythagorean theorem.

So, you're first point is 5 units away from point D and the second is -5 units from point D. These points are (2,2) and (12,2).

Here is a simple applet illustrating the relationship between perpendicular lines.

## Triangle Constructions:

## Sequence Applet:

## Transformation Applet:

Screen cast construction with Geogebra 3D

!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">Winter Break Challenge## vectors

## Parallelogram from Midpoints

## parallelogram 1

Parallelogram Proofs ChallengePage 37,problem 2 : It is given that ABCD and PBQD are parallelograms. Which of the numbered angles must be the same size as the angle numbered 1?The angle numbers that are highlighted in red all should be the same size as angle number 1.

This can is true because when two parallel lines are cut by a transversal line, their alternate interior angles should be the same. All the high lighted angles are congruent because angle 4 is the alternate angle of 1, 7 is the alternate angle of 4, 9 is the alternate of 7, 12 is the alternate of 9, 15 is the alternate of 12, which then leads back to angle 1 being the alternate angle of 15.

## Spider Man Problem