Table of Contents
Introduction ................................................................................................... i–iv
What is Engaging Mathematics, Volume I: Geometry? ......................................... iii
What is found in an Engaging Mathematics TEKS-based activity? .......................... iv
Coordinate and transformational geometry .................................................. 2–29
Fractional Distances on a Segment, Activity 1 G(2)(A) ........................................ 2
Fractional Distances on a Segment, Activity 2 G(2)(A) ........................................ 4
Slope, Distance, and Midpoint Formulas, Activity 1 G(2)(B) ................................. 6
Slope, Distance, and Midpoint Formulas, Activity 2 G(2)(B) ................................. 8
Parallel and Perpendicular Lines through a Point G(2)(C) ................................... 10
Transformations and Coordinate Notation, Activity 1 G(3)(A) .............................. 14
Transformations and Coordinate Notation, Activity 2 G(3)(A) .............................. 16
Composition of Transformations, Activity 1 G(3)(B) ........................................... 18
Composition of Transformations, Activity 2 G(3)(B) ........................................... 22
Composition of Transformations, Activity 3 G(3)(B) ........................................... 24
Sequences of Transformations G(3)(C) ............................................................ 26
Reflectional and Rotational Symmetry G(3)(D) ................................................. 28
Logical arguments and constructions ......................................................... 30–65
Logical Argument, Activity 1 G(4)(A) .............................................................. 30
Logical Argument, Activity 2 G(4)(A) .............................................................. 32
Deductive Reasoning, Activity 1 G(4)(B) .......................................................... 36
Deductive Reasoning, Activity 2 G(4)(B) .......................................................... 40
Counterexamples, Activity 1 G(4)(C) .............................................................. 42
Counterexamples, Activity 2 G(4)(C) .............................................................. 46
Euclidean and Spherical Geometries G(4)(D) .................................................... 50
Making Conjectures about Figures, Activity 1 G(5)(A) ........................................ 54
Making Conjectures about Figures, Activity 2 G(5)(A) ........................................ 56
Constructions G(5)(B) ................................................................................... 58
Conjectures from Constructions G(5)(C) .......................................................... 62
Triangle Inequality Theorem G(5)(D) .............................................................. 64
Proof and congruence .............................................................................. 66–100
Angle Relationships, Activity 1 G(6)(A) ............................................................ 66
Angle Relationships, Activity 2 G(6)(A) ............................................................ 68
Triangle Congruence, Activity 1 G(6)(B) .......................................................... 70
Triangle Congruence, Activity 2 G(6)(B) .......................................................... 74
Triangle Congruence, Activity 3 G(6)(B) .......................................................... 76
Rigid Transformations and Congruence G(6)(C) ................................................ 78
Relationships in Triangles, Activity 1 G(6)(D) ................................................... 80
Relationships in Triangles, Activity 2 G(6)(D) ................................................... 82
Relationships in Triangles, Activity 3 G(6)(D) ................................................... 84
Relationships in Triangles, Activity 4 G(6)(D) ................................................... 88
Quadrilaterals, Activity 1 G(6)(E) ................................................................... 92
Quadrilaterals, Activity 2 G(6)(E) ................................................................... 94
Quadrilaterals, Activity 3 G(6)(E) ................................................................... 96
Quadrilaterals, Activity 4 G(6)(E) ................................................................... 98
Similarity, proof, and trigonometry ........................................................ 102–141
Similar Triangles, Activity 1 G(7)(A) ............................................................. 102
Similar Triangles, Activity 2 G(7)(B) ............................................................. 104
Similar Triangles, Activity 3 G(7)(B) ............................................................. 106
Similar Triangles, Activity 4 G(8)(A) ............................................................. 110
Introduction ................................................................................................... i–iv
What is Engaging Mathematics, Volume I: Geometry? ......................................... iii
What is found in an Engaging Mathematics TEKS-based activity? .......................... iv
Coordinate and transformational geometry .................................................. 2–29
Fractional Distances on a Segment, Activity 1 G(2)(A) ........................................ 2
Fractional Distances on a Segment, Activity 2 G(2)(A) ........................................ 4
Slope, Distance, and Midpoint Formulas, Activity 1 G(2)(B) ................................. 6
Slope, Distance, and Midpoint Formulas, Activity 2 G(2)(B) ................................. 8
Parallel and Perpendicular Lines through a Point G(2)(C) ................................... 10
Transformations and Coordinate Notation, Activity 1 G(3)(A) .............................. 14
Transformations and Coordinate Notation, Activity 2 G(3)(A) .............................. 16
Composition of Transformations, Activity 1 G(3)(B) ........................................... 18
Composition of Transformations, Activity 2 G(3)(B) ........................................... 22
Composition of Transformations, Activity 3 G(3)(B) ........................................... 24
Sequences of Transformations G(3)(C) ............................................................ 26
Reflectional and Rotational Symmetry G(3)(D) ................................................. 28
Logical arguments and constructions ......................................................... 30–65
Logical Argument, Activity 1 G(4)(A) .............................................................. 30
Logical Argument, Activity 2 G(4)(A) .............................................................. 32
Deductive Reasoning, Activity 1 G(4)(B) .......................................................... 36
Deductive Reasoning, Activity 2 G(4)(B) .......................................................... 40
Counterexamples, Activity 1 G(4)(C) .............................................................. 42
Counterexamples, Activity 2 G(4)(C) .............................................................. 46
Euclidean and Spherical Geometries G(4)(D) .................................................... 50
Making Conjectures about Figures, Activity 1 G(5)(A) ........................................ 54
Making Conjectures about Figures, Activity 2 G(5)(A) ........................................ 56
Constructions G(5)(B) ................................................................................... 58
Conjectures from Constructions G(5)(C) .......................................................... 62
Triangle Inequality Theorem G(5)(D) .............................................................. 64
Proof and congruence .............................................................................. 66–100
Angle Relationships, Activity 1 G(6)(A) ............................................................ 66
Angle Relationships, Activity 2 G(6)(A) ............................................................ 68
Triangle Congruence, Activity 1 G(6)(B) .......................................................... 70
Triangle Congruence, Activity 2 G(6)(B) .......................................................... 74
Triangle Congruence, Activity 3 G(6)(B) .......................................................... 76
Rigid Transformations and Congruence G(6)(C) ................................................ 78
Relationships in Triangles, Activity 1 G(6)(D) ................................................... 80
Relationships in Triangles, Activity 2 G(6)(D) ................................................... 82
Relationships in Triangles, Activity 3 G(6)(D) ................................................... 84
Relationships in Triangles, Activity 4 G(6)(D) ................................................... 88
Quadrilaterals, Activity 1 G(6)(E) ................................................................... 92
Quadrilaterals, Activity 2 G(6)(E) ................................................................... 94
Quadrilaterals, Activity 3 G(6)(E) ................................................................... 96
Quadrilaterals, Activity 4 G(6)(E) ................................................................... 98
Similarity, proof, and trigonometry ........................................................ 102–141
Similar Triangles, Activity 1 G(7)(A) ............................................................. 102
Similar Triangles, Activity 2 G(7)(B) ............................................................. 104
Similar Triangles, Activity 3 G(7)(B) ............................................................. 106
Similar Triangles, Activity 4 G(8)(A) ............................................................. 110
