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APS Geometry Unit 6 Book

Wendy Sanchez, Feb 17, 2019

The GSE standards addressed in this book are: Translate between the geometric description and the equation for a conic section 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. Use coordinates to prove simple geometric theorems algebraically 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.

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
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
MGSE9-12G.GPE5
1. MGSE9-12.G.GPE.5: Activity 1 Sketch APS
2. MGSE9-12.G.GPE.5: Activity 2 APS
MGSE-12G.GPE6
1. Partitioned line segment--example APS
2. Partitioned line segment--general APS
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

Information

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.

1.2.

1.3.

2.

MGSE9-12G.GPE4

2.1.

Quads on Coordinate Plane 1 APS

Show that Figure ABCD is a rhombus.

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? 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? 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? 4. Now use the slope setting to find the slopes of all 3 lines. What do you notice? 5. Based on your answers to these questions, write a rule about the slopes of lines that are parallel.