APS Geometry Unit 6 Book

Wendy Sanchez, Feb 17, 2019

The GSE standards addressed in this book are: [b]Translate between the geometric description and the equation for a conic section[/b] MGSE9-12.G.GPE.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. [b]Use coordinates to prove simple geometric theorems algebraically [/b] MGSE9-12.G.GPE.4 Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0,2). (Focus on quadrilaterals, right triangles, and circles.) MGSE9-12.G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). MGSE9-12.G.GPE.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio. MGSE9-12.G.GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

Table of Contents

  1. MGSE9-12.G.GPE.1
    1. MGSE9-12.G.GPE.1 Investigation 1: Circles and the Pythagorean Theorem APS
    2. MGSE9-12.G.GPE.1 Investigation 1: Equation of a Circle Sketch APS
    3. MGSE9-12.G.GPE.1 Investigation 2: The Equation of a Circle APS
  2. MGSE9-12G.GPE4
    1. Quads on Coordinate Plane 1 APS
    2. Quad on Coordinate Plane 2 APS
    3. Quad on Coordinate Plane 3. APS
    4. Quad on Coordinate Plane 4. APS
    5. Quad on Coordinate Plane 5. APS
    6. Quad on Coordinate Plane 6. APS
    7. Quad on Coordinate Plane 7. APS
  3. MGSE9-12G.GPE5
    1. MGSE9-12.G.GPE.5: Activity 1 Sketch APS
    2. MGSE9-12.G.GPE.5: Activity 2 APS
  4. MGSE-12G.GPE6
    1. Partitioned line segment--example APS
    2. Partitioned line segment--general APS
  5. MGSE9-12G.GPE7
    1. Area and Perimeter of Triangle 1 APS
    2. Area and Perimeter of Triangle #2 APS
    3. Area and Perimeter of Rectangle 1 APS
    4. Area and Perimeter of Rectangle 2 APS

1.

MGSE9-12.G.GPE.1

Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

  • 1. MGSE9-12.G.GPE.1 Investigation 1: Circles and the Pythagorean Theorem APS
  • 2. MGSE9-12.G.GPE.1 Investigation 1: Equation of a Circle Sketch APS
  • 3. MGSE9-12.G.GPE.1 Investigation 2: The Equation of a Circle APS

1.1.

MGSE9-12.G.GPE.1 Investigation 1: Circles and the Pythagorean Theorem APS

Google Doc Link
https://docs.google.com/document/d/1y_ETCyYvXeuMtlZRHhNbKRib9UMVC1TcRRh0MUZRewQ/edit?usp=sharing
Circles and the Pythagorean Theorem PDF
Recall that the Pythagorean Theorem can be used to find the distance from one point to another by drawing a right triangle and solving for the hypotenuse. Use the Pythagorean Theorem to find the length of the radius of a circle given a point on the circle and the center of the circle. [br]
– Wendy Sanchez

1.2.

–

1.3.

–

2.

MGSE9-12G.GPE4

  • 1. Quads on Coordinate Plane 1 APS
  • 2. Quad on Coordinate Plane 2 APS
  • 3. Quad on Coordinate Plane 3. APS
  • 4. Quad on Coordinate Plane 4. APS
  • 5. Quad on Coordinate Plane 5. APS
  • 6. Quad on Coordinate Plane 6. APS
  • 7. Quad on Coordinate Plane 7. APS

2.1.

Quads on Coordinate Plane 1 APS

Show that Figure ABCD is a rhombus.
– Wendy Sanchez

2.2.

–

2.3.

–

2.4.

–

2.5.

–

2.6.

–

2.7.

–

3.

MGSE9-12G.GPE5

  • 1. MGSE9-12.G.GPE.5: Activity 1 Sketch APS
  • 2. MGSE9-12.G.GPE.5: Activity 2 APS

3.1.

MGSE9-12.G.GPE.5: Activity 1 Sketch APS

Activity 1 Questions
1. Focus on Line 1 and Line 2. Use Geogebra to measure the distance between A and C and the between B and D. What do you notice? Are Line 1 and Line 2 parallel, perpendicular, or oblique?[br][br]2. Focus on Line 2 and Line 3. Use Geogebra to measure the distance between C and E and between D and F. What do you notice? Are Line 2 and Line 3 parallel, perpendicular, or oblique?[br][br]3. Focus on Line 1 and Line 3. Use Geogebra to measure the distance between A and E and between B and F. What do you notice? Are Line 1 and Line 3 parallel, perpendicular, or oblique?[br][br]4. Now use the slope setting to find the slopes of all 3 lines. What do you notice? [br][br]5. Based on your answers to these questions, write a rule about the slopes of lines that are parallel.
Activity 1 Questions MGSE9-12G.GPE5 Google Doc
https://docs.google.com/document/d/10YRlRXTJWXU5CGBdSZizHOSlYADTsuttJmorXl8i_S8/edit?usp=sharing
Activity 1 Questions MGSE9-12G.GPE5
– Wendy Sanchez

3.2.

–

4.

MGSE-12G.GPE6

  • 1. Partitioned line segment--example APS
  • 2. Partitioned line segment--general APS

4.1.

Partitioned line segment--example APS

Partitioning a Segment-Specific
Partitioning a Segment-Specific Google Doc
https://docs.google.com/document/d/1xsVPLjG3Hkbi-AyfO67QrS5i4ylk-Kdd33qkzicmZT4/edit?usp=sharing
– Wendy Sanchez

4.2.

–

5.

MGSE9-12G.GPE7

  • 1. Area and Perimeter of Triangle 1 APS
  • 2. Area and Perimeter of Triangle #2 APS
  • 3. Area and Perimeter of Rectangle 1 APS
  • 4. Area and Perimeter of Rectangle 2 APS

5.1.

Area and Perimeter of Triangle 1 APS

– Wendy Sanchez, Bernard Smith

5.2.

–

5.3.

–

5.4.

–

Information