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UC MAT Geometry

Page history last edited by Kelly Stidham 1 yr ago

This is where we will store our work for Geometry

 

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Geometry Mathlets

 

Document Who? Notes
Drag Test Steve Phelps This mathlet is intended to illustrate the concept of a DRAG TEST, and what it means for a construction to "Pass the Drag Test."
Parallel Line Steve Phelps Do you think you can construct a parallel line without using the parallel line button? Give it a try!
Tessellate a Triangle Kelly Shattuck Discover how to tessellate a plane using only rotations and translations of a single triangle.
Angle Sums for Triangles Kelly Shattuck This mathlet allows students to prove that the sum of the interior angles of a triangle is equal to 180*.
Exterior Angles Sum for Triangles Kelly Shattuck What is the sum of the exterior angles of a triangle?  Use this mathlet to discover the answer.  Be sure to test your conjecture.
Signed Dilation of two circles Steve Blaylock Given two circles can you find the centers of dilation?  What is r for both centers?
Finding the Center of rotation Steve Blaylock Given 3 points and their image you can find the center of rotation
Triangulation Steve Blaylock Given three points and the distance from each point, you can find the point where each intersect
Theorem 5.2.1 Triangle Area Formula Christy Bredestege Begin with parallel lines,  two points on one line and one on the other.  See how the area changes as one vertex is moved around.
Centroids with medial triangles Christy Bredestege This is a picture of Exam question #2.  Someone, who shall remain nameless, missed it and I thought that I would draw a picture for her.
Theorem 5.7.4 Illustration Mindy Burcham This illustrates the theorem that relates parallelism to the area of a triangle.  If the vertices of a triangle are on parallel lines with one side fixed, why does the area remain the same, even though the side lengths change?
Perigal's dissection proof of Pythagora's Theorem with an Isosceles Triangle. Kelly Harms This begin's Perigal's dissection proof of the Pythagorean Theorem by first looking at an isosceles right triangle.  Why do the areas of the two smaller squares add up to the area of the larger square?
Equidistant Point Construction Jillian Maher This applet is from the Geometry textbook page 48, Exercise 3.10.4.  The goal is to construct a point on a line that is equidistant from two arbitrary points.
Excercise 5.5 Dissection of Pythagorean Theorem Kelly Harms  This illustrates Perigal's Proof of Pythagora's Theorem.  The follow up questions from Geometry I book Exercise 5.5 are included.
Perigal's proof of Pythagoras' Theorem Mindy Burcham There are several proofs of Pythagoras' Theorem.  This illustrates Perigal's proof of it.  This will walk you through the step by step construction of the proof. 
Theorem 2.4.3 Kelly Shattuck How can you tell if a quadrilateral is orthodiagonal?  This applet will help you discover the answer.
Construct the Centroid of a Quadrilateral Kelly Shattuck This applet will show help you to construct the centroid of a quadrilateral.
Trianlge Sum theorem Carey Costello Interactive to show the Triangle sum theorem.
incircleoftriangle.html Michael Smith Incircle of a triangle
Similar Triangles Final Exam Question Kelly Harms Another proof of similar triangles using similar ratios of sides.
Dilations and Translations do no Commute Steve Phelps This little applet illustrates a property of dilations and translations discussed in Geometry with Dr. Minda!
Dilations and Translations are Dilations Steve Phelps This little applet illustrates another property of dilations and translations discussed in Geometry with Dr. Minda!
Composition of Transformations Catherine O'Neill This sketch shows the composition of a translation and a dilation in either order.  Students are asked to find both centers and dilation factors.
Basic Translations Todd Majestic Simple picture asking students to find the centers of dilations and rotations
Creating Parallelograms Catherine O'Neill This sketch has students using rotations and medial triangles and how they relate to make parallelograms.

Similar quadrilaterals from a class discussion

 

Thales, Triangles, Congruency

 

Thales and Varignon

 Darron Steele

Yes; when you draw lines connecting corresponding points on similar quadrilaterals, they do intersect at one point.

 

See two illustrations of how these all play out with triangles, circles, and quadrilaterals.

 

 

Geometry 1: 5.7 Problem 4

 Mindy Burcham This is an illustration of the side-splitting theorem within the parallelogram.  This corresponds to a problem in the Geometry 1 notes.
Alternate Interior Angle Proof Carey Costello

This applet demonstrates the alternate interior angle theorem.
Area of Circles Observation Brian Bisignani An observation of the areas of circles using inscribed polygons.
Estimating Pi Brian Bisignani Similar to the one above, this applet uses both inscribed and circumscribed polygons to discover an estimate for pi from above and below.
Pythagorean Theorem Proof Brian Bisignani Demonstrates a standard proof of the Pythagorean Theorem, with questions to think about.
Nine-Point Circle Activity Brian Bisignani Nine-point circle observations and explorations.
Corresponding Angles Proof Kelly Shattuck Use vectors to see that corresponding angles are congruent.
Inscribed Circle of a Triangle Teresa Munninghoff Here I constructed the inscribed circle for a triangle. Examine the points that form the triangle and try dragging them around. Think about why this works. 
Triangle Tiling Tool Kelly Stidham This sketch includes a custom tool for half-turns of triangles about the midpoint on one of its sides.  The sketch is color coded by side and the triangle sides are dynamic.
geometry hw p.77 #3 Mary Liz Lamb This is the diagram for finding the dilatation mappings.
three point circle Mary Liz Lamb This constructs the circle through three given points
Circle Construction Jillian Maher  This applet shows the construction of a circle using only lines.  There is also space to do the construction yourself.  This applet is really a demonstration of a portion of Thales Theorem.
Chord Relationships Carey Costello This applet helps you find a relationship between the chords of two specific circles.
Centroid Dilation Veronica Robinson This applet lets you explore signed dilations of the vertices of a triangle about the centroid.
Euler Line Veronica Robinson This applet lets you explore the Euler Line.
July 22 homework problem Mary Liz Lamb this is one of the geometry problems from the July 22 homework.
Triangulation Theorem Jere Issenmann This shows the picture of 3 point Triangulation Theorem shown in class:)
Page 41 question #4 Linda Johnson Here is a picture for the homework question
Triangle reflections Linda Johnson Look at the reflections about the medians of a triangle.  Can you make the triangles coincide?
page 122 question 3 picture Linda Johnson Here is a pic for the homework question!
Varignon's Parallelogram lbollman This mathlet  illustrates Varignon's Parallelogram.
Pythagorean Theorem lbollman This mathlet illustrates Pythagorean Theorem.
Regular hexagon yields a regular triangle Brad McDaniel Look at how a regular hexagon yeilds a regular triangle.
Right Triangles and Circles Teresa Munninghoff This applet explores a right triangle inscribed in a circle.
Area of two triangles Teresa Munninghoff This applet explores two triangles that share a base and the line through the other vertices is parallel to the base. What do you notice about the areas of the triangles?
Dilating the Euler Line Holly Phelps This activity lets you dilating a triangle and its Euler line to see if it is preserved with a dilation.
Symmetries of a Square Kelly Shattuck A square has 8 symmetries. This applet will show the mapping of each vertex under each of these transformations.
Regular Hexagon Yeilds Regular Triangle Brad McDaniel Make a conjecture about the given picture.
Equilateral Triangle and Interior Angles Brad McDaniel Make a conjecture about the given picture.
Remote Interior Angles Sum and Exterior Angle Brad McDaniel Make a conjecture about the given picture.
Glide Reflection of Sine Melissa Keller See what happens to Sine after a glide reflection
Slope and Line Reflections Holly Phelps This is an activity to explore what happens to the slope of a refelcted line and it's equation in relationship with the original line.
Unit Vector Polygon Isometries Catherine O'Neill This worksheet explores isometries of the unit square and asks students to compare lines of reflection for different quadrilaterals.
Nine Point Circle Todd Majestic This applet shows the 9-pt circle that we talked about in class
Lines Symmetries of a Rectangle Christy Bredestege This gives a basic interpretation of lines of symmetry for any rectangle.
Inscribing a Quadrilateral in a Circle Jackie Southard See how the perpendicular bisectors of the sides relate to the ability to inscribe a quadrilateral in a circle.
Pythagorean Theorem Jackie Southard This is a visualization of Pelikan's favorite Pythagorean Theorem proof. 
Side Splitter Jana Rae Debord Demonstrates the proportional sides of triangle with a parallel line to a base.
Isometries can be found by glide reflections or rotations Jackie Southard This shows how all isometries can be found by a glide reflection or a rotation based on whether or not the isometry is orientation preserving.
Theorem 5.7.4 Michael Smith Applet showing proof of Theorem 5.7.4 from Geometry 1 notes
Triangles Michael Smith Applet for teaching sum of measure of angles
Midpoint Connector Theorem Michael Smith Applet demonstrating Midpoint Connector Theorem
Angles Michael Smith Applet for teaching complimentary and supplementary angles
Angles in Polygons Michael Smith Applet for teaching sum of angles in polygons
Miquel's Theorem Michael Smith Applet that shows the three circles that can be constructed through points on two sides of a triangle and in the inclusive vertices have a point that is concurrent.
Area of a Triangle Beth Jordan Change the shape of the triangle and notice what happens to the area.
Rotating the Centroid Holly Phelps This is an applet to show that the centroid is preserved when rotating a triangle.
Orthogonal Projection Theorem Beth Jordan Applet fo rthe Orthogonal Projection of a Point onto a line.
Triangle Inequality Beth Jordan Use this applet to change the triangle and prove the triangle inequality theorem.
Find the Isometry Melissa Keller Use this in conjunction with homework from 8-8-08
Angle Sum Melissa Keller Students prove why interior angles of a triangle sum to 180 using exterior angles
Circle and Triangle Centroid Melissa Keller Drag point E to see what happens to the centroid
Exam I #3 Melissa Keller Sketch for Exam 1 problem 3
Square symmetries: Reflections
 Kelly Stidham High School version of Geometry Example
Square Symmetries: Rotations
 Kelly Stidham
High School version of Geometry Example

 

Comments (2)

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donhawkins@... said

at 11:05 am on Jun 22, 2008

Does this work?

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donhawkins@... said

at 11:07 am on Jun 22, 2008

How can this program best be applied to secondary school applications?

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