APS Geometry Unit 3 Book

Wendy Sanchez, May 9, 2019

Understand similarity in terms of similarity transformations MGSE9-12.G.SRT.1 Verify experimentally the properties of dilations given by a center and a scale factor. a. The dilation of a line not passing through the center of the dilation results in a parallel line and leaves a line passing through the center unchanged. b. The dilation of a line segment is longer or shorter according to the ratio given by the scale factor. MGSE9-12.G.SRT.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain, using similarity transformations, the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. MGSE9-12.G.SRT.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. Prove theorems involving similarity MGSE9-12.G.SRT.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, (and its converse); the Pythagorean Theorem using triangle similarity. MGSE9-12.G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Understand and apply theorems about circles MGSE9-12.G.C.1 Understand that all circles are similar.

Table of Contents

  1. MGSE9-12.G.SRT.1
    1. Dilations Exploration APS
  2. MGSE9-12.G.SRT.2
    1. Proving Triangles Similar (1) APS
    2. Proving Triangles Similar (2) APS
    3. Proving Triangles Similar (3) APS
    4. Proving Triangles Similar (4) APS
  3. MGSE9-12.G.SRT.3
  4. MGSE9-12.G.SRT.4
    1. Parallel sides cut proportionally APS
  5. MGSE9-12.G.SRT.5
  6. MGSE9-12.G.C.1

1.

MGSE9-12.G.SRT.1

  • 1. Dilations Exploration APS

1.1.

Dilations Exploration APS

Drag point O to change the center of the dilation. Drag points A, B, or C to change the pre-image. To change the dilation factor, enter a number between 0 and 3 and hit enter.
1) Move the center of dilation point O to point A. Change the dilation factor to any number between 0 & 3 and see what happens.[br]2) Move the center of dilation point O to point B. Change the dilation factor to any number between 0 & 3 and see what happens.[br]3) Move the center of dilation point O to point C. Change the dilation factor to any number between 0 & 3 and see what happens.[br]4) Move the center of dilation point O to the center of the pre-image. Change the dilation factor to any number between 0 & 3 and see what happens.[br]5) What does a dilation factor of 1 do?[br]6) What does the dilation factor greater than 1 do?[br]7) What does then dilation factor less than 1 do?
– S Sharma, Shane Canale

2.

MGSE9-12.G.SRT.2

  • 1. Proving Triangles Similar (1) APS
  • 2. Proving Triangles Similar (2) APS
  • 3. Proving Triangles Similar (3) APS
  • 4. Proving Triangles Similar (4) APS

2.1.

Proving Triangles Similar (1) APS

Directions
Use a series of transformations to try to map the green triangle onto the bigger triangle. Try to use the fewest moves possible!
– Wendy Sanchez

2.2.

–

2.3.

–

2.4.

–

3.

MGSE9-12.G.SRT.3


    This chapter does not contain any resources yet.

4.

MGSE9-12.G.SRT.4

  • 1. Parallel sides cut proportionally APS

4.1.

Parallel sides cut proportionally APS

Directions
Move point D along segment AC. Notice the slopes (shown in red) of segments DE and AB (what does this tell you about lines DE and AB? What happens to the ratios [math]\frac{CD}{DA}[/math] and [math]\frac{CE}{EB}[/math] as you move point D?
– Wendy Sanchez

5.

MGSE9-12.G.SRT.5


    This chapter does not contain any resources yet.

6.

MGSE9-12.G.C.1


    This chapter does not contain any resources yet.

Information