Eureka Geometry Mod. 1 Congruence, Proof, and Constructions
Eureka Geometry Module 1 Congruence, Proof, and Constructions
Table of Contents
- Module 1A - Basic Constructions
- 1.02 How to Construct Hexagon
- 1.03 How to Construct an Angle Bisector
- 1.03 How to Construct a Congruent Angle
- 1.05 Exploratory Challenge Day 2
- 1.05 Day 1 Exercises
- 1.05 Homework
- How to Construct a Perpendicular Bisector
- Module 1B - Unknown Angles
- Adjacent Angles
- Angles at a point
- Vertical angles
- Linear Pairs
- 1.08 Day 1 Classify Triangles
- 1.08 Day 2 Triangle Angle-Sum Theorem
- 1.08 Day 2 Triangles do add up to 180°!
- 1.08 Day 3 Exterior Angle Theorem
- 1.08 Day 1 Exploration
- Triangle Sum Theorem
- 1.07 Day 2
- 1.07 Day 1
- Alternate Exterior and Alternate Interior Angles
- Corresponding Angles
- 1.06 Angle investigation
- Module 1C - Transformations / Rigid Motions
- New Aperiodic Monotile!
- Module 1C Review
- 1.16 Translations
- 1.15 Rotational Symmetry
- Thanksgiving Rotation Exploration
- 1.13 Rotation Exploration
- Snowflake Designer
- Module 1D Congruence
- 1.26 Activity
- 1.25 - HL Practice
- 1.25 AAA Exploration
- 1.24 Exploration
- ASA: Exercise
- 1.23 Classwork
- 1.22 Congruence Criteria for Triangles - SAS
- Module 1E Proving Properties of Geometric Figures
- Poorly Drawn Quadrilaterals
- 1.30 Centroid Warm-Up
- 1.30 Construct a Centroid
- 1.29 Medial Triangle
- 1.29 Midsegment of a Triangle (r1)
- 1.28 Properties of a Rectangle and Square
- 1.28 Properties of a Rhombus
- 1.28 Properties of a Parallelogram
- Medians Centroid Theorem (Proof without Words)
- Parallelogram Theorems: Quick Check-in
- Module 1F Advanced Constructions
- Construct a Square, Given a Side
1.02 How to Construct Hexagon
Click the checked boxes in order below to see how to construct a hexagon.
Now you try. Construct a hexagon.
Adjacent Angles
Angles on opposite sides of a common arm are called adjacent angles.[br][i]AD[/i] is the common arm.
New Aperiodic Monotile!
[size=150]This construction was based upon a new awesome discovery by David Smith, Joseph Samuel Meyers, Craig S. Kaplan, and Chaim Goodman-Strauss. [/size]
[size=150]The tile you see below is an [b]aperiodic tile[/b]. That is, it is possible to entirely cover your screen with these tiles [b]in such a way that they do not repeat in any pattern, nor with any rhyme or reason! [br][/b][br][i]There is no other single tile that has yet been discovered that can do this. [br]This is the first of its kind! [/i][/size]
[size=200][b][color=#1e84cc][url=https://www.geogebra.org/classic/gq5mtkfa]Click here for a much larger, full-screen version where you can create & save your own tessellation![/url][/color][/b][/size]
Click on the custom monotile tools below to create more! Select the MOVE tool (arrow) to move and spin them around!
More info re: this cool discovery can be found [url=https://arxiv.org/abs/2303.10798]here[/url] and [url=https://arxiv.org/pdf/2303.10798.pdf]here[/url].
1.26 Activity
Complete the congruence statement: DEF is congruent to _____. To complete the congruence statement, we must match the corresponding vertices of the two triangles.
What vertex corresponds to vertex D? [br][br]Hint: Look for a vertex with matching marks - red line(s) or no red line.[br]
What vertex corresponds to vertex E? [br][br]Hint: Look for a vertex with matching marks - red line(s) or no red line.[br]
What vertex corresponds to vertex F? [br][br]Hint: Look for a vertex with matching marks - red line(s) or no red line.[br]
Complete the congruence statement on the line below.[br]DEF is congruent to _____
Complete the congruence statement: BCD is congruent to _____. To complete the congruence statement, we must match the corresponding vertices of the two triangles.
What vertex corresponds to vertex B? [br][br]Hint: Look for a vertex with matching marks on the opposite side - ||, |||, or |||.[br]
What vertex corresponds to vertex C? [br][br]Hint: Look for a vertex with matching marks on the opposite side - ||, |||, or |||.[br]
What vertex corresponds to vertex D? [br][br]Hint: Look for a vertex with matching marks on the opposite side - ||, |||, or |||.[br]
Complete the congruence statement on the line below.[br]BCD is congruent to _____
Poorly Drawn Quadrilaterals
Determine the best possible name for the poorly drawn quadrilateral below. Base your reasoning on how the quadrilateral is marked, and not on how it looks. Check your answer. Some quadrilaterals can not be determined, and others may be impossible!
Construct a Square, Given a Side
STUDENTS:
Use the tools in the applet to construct a square with AB as one of its sides.[br][br]Explore. Try to do this on your own.[br]If you need more help, there are detailed instructions and a video at the bottom.
How to Construct a Square
You start with segment AB.[br]Use the LINE tool to make this line AB.[br][br]Use the compass tool to make a circle from A to B (Center is at A).[br]Mark the other intersection as point C. [br]Segments AB and AC are congruent because both are radii of circle A.[br][br]Construct two more circles. One is from C to B. The other is from B to C.[br]Mark the points where these two circles intersect as D (on top) and E (on bottom).[br]DE is the perpendicular bisector of segment BC. They intersect at right angles.[br]This is important, because this will make part of our square.[br][br]Mark the intersection of circle A and segment DA. Call it F. AF and AB are two sides of the square.[br][br]Finally, make two more circles and their intersection: from D to A and from B to A. Call the intersection G.[br][br]You should have ABGF is a square. [br]Use the POLYGON tool to make it a square.[br][br]Do the DRAG TEST to verify it is a square.
Construct a Square, Given a Side
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