CCSS High School: Geometry (Expressing GEO. Prop's w/Equns.)
[b]This GeoGebra Book contains lots of discovery-based learning activities, investigations, and meaningful remediation worksheets that were designed to help enhance students' learning of geometry concepts both inside and outside of the mathematics classroom. [color=#1551b5]This GeoGebra Book also contains contributions from Samantha Cruz ([url]https://www.geogebra.org/scruz10[/url])[/color] [/b]
Table of Contents
- HSG.GPE.A.1
- Circle Equation: Center (0,0)
- Circle Equation: Center NOT (0,0)
- Circle Equation: Center (h,k)
- Equation & Graph of a Circle
- HSG.GPE.A.2
- Locus Problem (1)
- Locus Construction 1
- Animation 85
- Parabola as a Locus
- Animation 4
- Locus Constructions (via Paper Folding)
- Parabola (Locus Construction)
- Parabola (Graph & Equation Anatomy)
- HSG.GPE.A.3
- Locus Problem (2)
- Locus Construction 2
- Ellipse (Locus Construction)
- Animation 86
- Ellipse: Magic Sum = ?
- Ellipse: Magic Sum = ? (V2)
- Animation 10
- Locus Problem (3)
- Locus Construction 3
- Animation 87
- Hyperbola: Difference = ?
- Animation 30
- Locus Constructions (via Paper Folding)
- Hyperbola (Locus Construction)
- HSG.GPE.B.4
- Parallelogram Creation Exercises (I)
- Parallelogram Creation Exercise (II)
- Parallelogram Creation Exercise (III)
- Parallelogram: Coordinate Geometry Setup
- Parallelogram Diagonals
- Isosceles Triangle Medians
- Rectangle Diagonals
- Isosceles Trapezoid Diagonals
- Isosceles Trapezoid Midpoints
- Rhombus Diagonals
- Inscribed Angle Intercepts Semicircle
- 3 Special Points!
- Finsler-Hadwiger Exercise (VA)
- Finsler-Hadwiger Exercise (VB)
- Slope to Angle Measure Calculator (I)
- Slope to Angle Measure Calculator (II)
- HSG.GPE.B.5
- Slope: Intuitive Introduction
- Parallel Consequence? (VA)
- Parallel Consequence? (VB)
- Perpendicular Lines Investigation (VA)
- Perpendicular Lines Investigation (VB)
- Slope Triangle Rotation (VA)
- Animation 103
- Parallel & Perpendicular Consequence
- Parallel Lines Definition
- Perpendicular Lines Definition (& Consequence)
- Writing Equations of Parallel and Perpendicular Lines
- HSG.GPE.B.6
- Endpoint (x,y) of a Segment Given Midpoint & Other Endpoint
- Midpoint (x,y) of a Segment in the Coordinate Plane (Quiz)
- Partition Line Segments
- HSG.GPE.B.7
- Distance in the Coordinate Plane (With Hints)
- Distance in the Coordinate Plane (II)
- Distance in the Coordinate Plane (Quiz without Grid)
- Distance in the Coordinate Plane (Quiz With Grid)
- Links to Other CCSS High School: Geometry Standards
- Geometry Resources
Circle Equation: Center (0,0)
For the questions below, be sure to zoom out if you need to!
1.
Suppose [i]P(x,y)[/i] = any point that lies on a circle with center (0,0) and radius 5. [br]Use what you've observed to write an equation that expresses the relationship among [i]x[/i], [i]y[/i], and [i]r[/i].
2.
What is the equation of a circle with center (0,0) and radius [i]r[/i] = 9?
3.
Suppose another circle has center (0,0). Suppose this circle also passes through the point (12, -5).[br]Write the equation of this circle. [br]
4. FINAL QUESTION:
Suppose [i]P(x,y)[/i] = any point that lies on a circle with center (0,0) and radius [i]r[/i], where [i]r[/i] > 0. [br]Use what you've observed to write an equation that expresses the relationship among [i]x[/i], [i]y[/i], and [i]r[/i].
Quick (Silent) Demo
Locus Problem (1)
In the applet below, [br][br][i][color=#1e84cc][b]F[/b][/color][/i][color=#1e84cc][b] is a point[/b] [/color]that is not on line [i]d[/i]. [br][b]Point [i]D[/i] is a point that lies ON [color=#666666]the line that passes through [i]A [/i]and [i]B[/i][/color]. [br][/b]The [color=#ff00ff][b]pink line[/b][/color] is the [color=#ff00ff][b]perpendicular bisector[/b][/color] of the segment with endpoints [i][color=#1e84cc][b]F[/b][/color][/i] and [i][b]D[/b][/i]. [br][br]Drag [b]point [i]D[/i][/b] along the line. What do you see? Describe in detail! [br] [br]Feel free to alter the locations of [color=#666666][i][b]A,[/b][/i][/color] [i][color=#666666][b]B[/b][/color], [/i]and/or [i][color=#1e84cc][b]F[/b][/color][/i][color=#666666]. [br][/color]Then [color=#38761d][b]clear the trace[/b][/color] and drag [b]point [i]D[/i][/b] along [color=#666666][b]the line[/b][/color] again. [br][br]Why does this occur?
Please go to the [url=https://www.geogebra.org/m/sduBXC6P]Locus Construction 1 Task[/url] and begin!
Locus Problem (2)
In the applet below, [br][br][color=#1e84cc][b][i]O[/i] is the center [/b][/color]of the circle shown. [br][b]Point [i]D[/i] is a point that lies ON this circle. [/b][br][color=#1e84cc][b]Point [i]A[/i] is a point that ALWAYS LIES INSIDE[/b] [/color]the circle. (You can move it anywhere you'd like). [br]The [color=#ff00ff][b]pink line[/b][/color] is the [color=#ff00ff][b]perpendicular bisector[/b][/color] of the segment with endpoints [i]A[/i] and [i]D[/i]. [br][br]Drag [b]point [i]D[/i][/b] around the circle a few times. What do you see? Describe in detail! [br] [br]Feel free to alter the locations of [i][color=#1e84cc][b]A[/b][/color][/i] and [i][color=#1e84cc][b]R[/b][/color]. [/i]Then clear the trace and drag [b]point [i]D[/i][/b] around again. [br][br]Why does this occur?
Please go to the [url=https://www.geogebra.org/m/TZu6tRwE]Locus Construction 2 Task[/url] & begin!
Parallelogram Creation Exercises (I)
[color=#000000]In the applets below, 3 vertices of a parallelogram are shown.[br]The coordinates (x,y) of these vertices are also displayed as well. [br][br]In each task below, determine the coordinates of each parallelogram's 4th vertex. [br]Plot this point in the coordinate plane. [br]Feel free to use any of the tools of the limited toolbar when doing so. [br]Then, use the Polygon tool to construct the parallelogram.[br][br]Afterwards, use any of the tools of each applet's limited toolbar to clearly show that the quadrilateral you've constructed is indeed a parallelogram. [/color]
Slope: Intuitive Introduction
[color=#000000]Discovery Lesson Activity: [br][/color][color=#980000][br][/color][b][color=#0000ff][url=https://docs.google.com/document/d/1W5fggl-QmnwOoT1Yjs2MfZnwVzIF49pflGX33xe0PN0/edit?usp=sharing]Slope: Intuitive Introduction Investigation [/url][/color][/b]
Endpoint (x,y) of a Segment Given Midpoint & Other Endpoint
[b][color=#c51414]Directions:[/color][/b][br][br]1) In the applet below, note the [color=#0a971e]segment [/color]with [color=#1551b5]endpoint B[/color] and [color=#c51414]MIDPOINT M[/color].[br]2) Algebraically determine the coordinates of the [color=#1551b5]other endpoint (x, y)[/color]. [br]3) [color=#1551b5]Enter in these coordinates in the input boxes provided in the upper left hand corner.[/color][br]4) If you get the problem correct, the applet will indicate this to you. If not, keep trying.[br]5) Click the "New Problem" button to create a new segment with different endpoints.[br]6) Repeat steps (1) - (5).[br][b]7) Repeat steps (5) - (7) as many times as you need in order to master this concept![/b]
Distance in the Coordinate Plane (With Hints)
Discovery Lesson (Can be used without interactive figure below)
Geometry Resources
[list][*][b][url=https://www.geogebra.org/m/z8nvD94T]Congruence (Volume 1)[/url][/b][/*][*][b][url=https://www.geogebra.org/m/munhXmzx]Congruence (Volume 2)[/url][/b][/*][*][b][url=https://www.geogebra.org/m/dPqv8ACE]Similarity, Right Triangles, Trigonometry[/url][/b][/*][*][b][url=https://www.geogebra.org/m/C7dutQHh]Circles[/url][/b][/*][*][b][url=https://www.geogebra.org/m/K2YbdFk8]Coordinate and Analytic Geometry[/url][/b][/*][*][b][url=https://www.geogebra.org/m/xDNjSjEK]Area, Surface Area, Volume, 3D, Cross Section[/url] [/b][/*][*][b][url=https://www.geogebra.org/m/NjmEPs3t]Proof Challenges[/url] [/b][/*][/list]