Outline
Congruence (CO) Cluster
MAFS.912.G-CO.1.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
MAFS.912.G-CO.1.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
MAFS.912.G-CO.1.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
MAFS.912.G-CO.1.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
MAFS.912.G-CO.1.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
MAFS.912.G-CO.2.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
MAFS.912.G-CO.2.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
MAFS.912.G-CO.2.8 Explain how the criteria for triangle congruence (ASA, SAS, SSS, and Hypotenuse-Leg) follow from the definition of congruence in terms of rigid motions.
MAFS.912.G-CO.3.9 Prove theorems about lines and angles; use theorems about lines and angles to solve problems. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segments endpoints.
MAFS.912.G-CO.3.10 Prove theorems about triangles; use theorems about triangles to solve problems. Theorems include: measures of interior angles of a triangle sum to 180 triangle inequality theorem; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
MAFS.912.G-CO.3.11 Prove theorems about parallelograms; use theorems about parallelograms to solve problems. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.
MAFS.912.G-CO.4.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
MAFS.912.G-CO.4.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
Table of Contents
MAFS.912.G-CO.1.1
- Congruent Segments: Quick Exploration
- Animation 18
- Proving Segments Congruent (Exercise)
- Congruent Angles: Definition
- Animation 36
- Proving Angles Congruent (1)
- Proving Angles Congruent (2)
- Proving Angles Congruent
- Midpoint Definition
- Animation 56
- Segment Bisector Definition
- Animation 160
- Perpendicular Lines: Quick Intro
- Segment Bisectors (Definitions)
- Perpendicular Bisector Definition
- Perpendicular Bisector Definition
- Animation 15
- Angle Bisector Definition (I)
- Complementary Meaning?
- Animation 48
- Supplementary Angles (Quick Exploration)
- Animation 19
- Circle vs. Sphere
- Triangle Altitude Illustrator and Definition Writing Prompt
- Animation 162
- Triangle Median Illustrator & Definition Writing Prompt
- Animation 161
- Equilateral Action!!!
- Animation 165
- Equiangular Action!!!
- Animation 166
- Regular Polygon Action!
- Animation 193
MAFS.912.G-CO.1.2, 1.3, 1.4, 1.5
- Translations and Rotations
- Translating Triangle by a Vector
- Reflections
- Reflections Introduction
- Flip Flop Reflection
- Tool for compositions of rigid transformations and dilations
- Applet for Multiple Transformations
- Messing With Lisa
- Rotations: Introduction
- Point Symmetry: Another Perspective
- Reflections and Translations
- Tessellation by Translation
- Parallel Translation
- Transformations: Exercise 1
- Transformations: Exercise 2
- Transformations: Exercise 3
MAFS.912.G-CO.2.6
MAFS.912.G-CO.2.7
MAFS.912.G-CO.2.8
MAFS.912.G-CO.3.9
- Proof Prompt (A)
- Animation 128
- Proof Prompt (B)
- Animation 127
- Proof Prompt (C)
- Animation 131
- Proof Prompt (D)
- Animation 130
- Vertical Angles Exploration (1)
- Vertical Angles Exploration (2)
- Vertical Angles Theorem
- Animation 1
- Transversal Intersects Parallel Lines
- Corresponding Angles: Quick Investigation
- Congruent Corresponding Angles to Start? (Quick Investigation)
- Exploring Corresponding Angles (V2)
- Alternate Interior Angles: Quick Investigation
- Alternate Interior Angles Theorem (V1)
- Exploring Alternate Interior Angles (V2)
- Alternate Interior Angles Theorem (V3)
- Animation 16
- Alternate Exterior Angles: Quick Investigation
- Alternate Exterior Angles Theorem (V1)
- Exploring Alternate Exterior Angles (V2)
- Animation 39
- Animation 60
- Same-Side-Interior Angles: Quick Investigation
- Same Side Interior Angles Theorem
- Animation 29
- Same-Side-Exterior Angles: Quick Investigation
- Exploring Same Side Exterior Angles
- Animation 73
- Solution to Parallel Lines & Angles Problem
- Interesting Coplanar Locations (1)
- A Special Theorem: Part 1 (V1)
- A Special Theorem: Part 2 (V1)
- A Special Theorem: Part 2 (V2)
- A Special Theorem: Part 2 (V3)
- Animation 57
- A Special Theorem: Part 2 (V4)
- PBT (Part 1) - Quick
- PBT (Part 2) - Quick
- Where in This City? (1)
- CT Home Depots
- Where in NYC? (VA)
- Where in NYC? (VB)
- Where in NYC? (VC)
- Angle Bisector Theorem (Part 1)
- Another Special Theorem: Part 1 (V1)
- Another Special Theorem: Part 2 (V1)
- Another Special Theorem: Part 1 (V2)
- Animation 58
- Another Special Theorem: Part 1 (V3)
- Effortless Trisections
- Animation 134
- Parallel Lines Congruent Segments Theorem
- Parallel Lines Proportionality Theorem
- Animation 135
MAFS.912.G-CO.3.10
- Triangle Area Action! (V1)
- Triangle Area Action!!! (V2)
- Animation 175
- Area of a Triangle (Discovery)
- 4 Triangles Action!!!
- Animation 179
- Triangle Angle Theorems
- Animation 171
- Triangle Angle Theorems (V2)
- Animation 2
- Triangle Angle Theorems (V3)
- Transformation Proof 3
- Triangle Angle Sum Theorem
- Obvious Corollary
- Animation 140
- Triangle Exterior Angle
- Animation 102
- Triangle: Exterior Angles
- Quadrilateral: Exterior Angles
- Pentagon: Exterior Angles
- Polygons: Exterior Angles
- Polygons: Exterior Angles - REVAMPED
- Exploring Polygon Angles: Triangle through Octagon
- Angles of a Right Triangle
- Animation 104
- Acute Angles of a Right Triangle
- Animation 129
- Animation 22
- Isosceles Triangle Theorem: Discovery Lab
- A Special Triangle & Its Properties (I)
- Animation 8
- Isosceles Triangle Investigation
- Converse of IST (V1)
- Animation 82
- Animation 23
- Another Special Triangle and its Properties (II)
- Animation 27
- Converse of IST (II)
- Animation 84
- Isosceles Right Triangle: Quick Investigation
- Special Right Triangle (I)
- Animation 59
- Special Right Triangle (II)
- Another Special Right Triangle (Guided Discovery)
- Animation 42
- Special Line through Triangle V1 (Theorem Discovery)
- Special Line through Triangle V2 (Theorem Discovery)
- Triangle Midsegment Action!
- Animation 141
- Midsegment of a Triangle
- Triangle Inequality: Discovery Lesson
- Triangle Side Possibilities? (V2)
- Triangle Inequality
- Triangle Inequality (II)
- Inequalities in 1 Triangle
- Points of Concurrency: Investigation
- Orthocenter Exploration
- Circumcenter (& Questions)
- Circumcenter & Circumcircle Action!
- Animation 28
- Midpoint of HYP
- Animation 46
- Incenter Exploration (A)
- Incenter Exploration (B)
- Incenter & Incircle Action!
- Animation 17
- Triangle Medians: Quick Investigation
- Medians Centroid Theorem (Proof without Words)
- Medians and Centroid Dance
- Animation 25
MAFS.912.G-CO.3.11
- Parallelogram: Area
- Animation 202
- Parallelogram Construction Template & Discovery Lab
- Parallelogram Template (Scaffolded Discovery)
- Parallelogram Template
- Parallelogram: Theorem 1
- Animation 123
- Parallelogram: Theorem 2
- Animation 124
- Parallelogram: Theorem (3)
- Animation 125
- Parallelograms (I)
- Animation 75
- Animation 80
- Animation 6
- What Kind of Quadrilateral is This? (Part 1)
- What Kind of Quadrilateral is This? (Part 2)
- What Kind of Quadrilateral is This? (Part 3)
- What Kind of Quadrilateral is This? (Part 4)
- Special Quadrilateral: Theorem 1
- Animation 184
- Special Quadrilateral: Theorem 2
- Animation 185
- Special Quadrilateral: Theorem 3
- Animation 186
- Special Quadrilateral: Theorem 4
- Animation 187
- Congruent Opposite Sides of a Quadrilateral
- Quadrilateral With Opposite Angles Congruent
- What Kind of Quad?
- Quadrilateral Investigation (I)
- Rhombus Action!
- Animation 11
- Rhombus Template (Scaffolded Discovery)
- Rhombus Template with Investigation Questions
- Rectangle Action!
- Animation 31
- Rectangle Template (Scaffolded Investigation)
- Rectangle Template with Investigation Questions
- Square Action!
- Animation 41
- Square Template (Scaffolded Investigation)
- Square Template with Investigation Questions
- Trapezoids: Median Investiagtion
- Trapezoid Median (Midsegment) Action!
- Animation 67
- Trapezoid Median: 2 Discoveries
- Isosceles Trapezoid Action!
- Animation 64
- Animation 35
- Isosceles Trapezoid Template (Scaffolded Discovery)
- Isosceles Trapezoid Template
- Animation 49
- Kite Action!
- Animation 26
- Kite Template: Scaffolded Investigation
- Kite Template with Investigation Questions
- Quad Midpoints Action!
- Animation 52
MAFS.912.G-CO.4.12
- Congruent Segments Construction (I)
- Isosceles Triangle (Quick Construction Technique) V1
- Animation 199
- Equilateral Triangle Construction (Dynamic Illustration)
- Animation 201
- Congruent Angle: Construction
- Congruent Angle Construction Action!
- Animation 196
- Angle Bisector Construction Action!
- Animation 197
- Alternate Angle Bisector Construction
- Animation 117
- Angle Bisector: Construction
- Angle Bisector (Basic Exercise)
- Perpendicular Line: Construction 1
- Perpendicular Line: Construction 2
- Perpendicular Bisector: Construction
- Parallel Line: Constructions
- Congruent Triangle: Construction
- Rectangle Construction Exercise
- Rectangle Construction Exercise: Revamped (V1)
- Rectangle Construction Exercise: Revamped (V2)
- Rhombus Construction Exercise: V1
- Rhombus Construction Exercise: V2
- Other Constructions: 1
- Other Constructions: 2
- Centroid Construction Challenge #1
- Possible Solution for Centroid Challenge #1
- Centroid Construction Challenge #2
- Possible Solution for Centroid Construction Challenge #2
- Centroid Construction Challenge #3
- Possible solution to Centroid Construction Challenge #3
- Triangle Construction Challenge #1
- Possible solution to Triangle Construction Challenge #1
- Triangle Consruction Challenge #2
- Possible solution to Triangle Construction Challenge #2
- Triangle Construction Challenge #3
- Potential solution for Triangle Construction Challenge #3
- Geometric Mean Illustration
- Animation 211
- Geometric Mean: Construction (VA)
- Geometric Mean: Construction (VB)
MAFS.912.G-CO.4.12