G-2: The student will demonstrate through the mathematical processes an understanding of the properties of basic geometric figures and the relationships between and among them.

G-2.2: Apply properties of parallel lines, intersecting lines, and parallel lines cut by a transversal to solve problems.

Constructing Congruent Segments and Angles
Parallel, Intersecting, and Skew Lines

G-2.3: Use the congruence of line segments and angles to solve problems.

Congruence in Right Triangles
Constructing Congruent Segments and Angles
Proving Triangles Congruent
Triangle Angle Sum

G-2.5: Carry out a procedure to create geometric constructions (including the midpoint of a line segment, the angle bisector, the perpendicular bisector of a line segment, the line through a given point that is parallel to a given line, and the line through a given point that is perpendicular to a given line).

3D and Orthographic Views
Constructing Congruent Segments and Angles
Constructing Parallel and Perpendicular Lines
Parallel, Intersecting, and Skew Lines
Segment and Angle Bisectors

G-2.6: Use scale factors to solve problems involving scale drawings and models.

Dilations
Perimeters and Areas of Similar Figures
Similar Figures

G-2.7: Use geometric probability to solve problems.

Geometric Probability

G-3: The student will demonstrate through the mathematical processes an understanding of the properties and special segments of triangles and the relationships between and among triangles.

G-3.1: Carry out a procedure to compute the perimeter of a triangle.

Perimeters and Areas of Similar Figures

G-3.2: Carry out a procedure to compute the area of a triangle.

Area of Triangles
Perimeters and Areas of Similar Figures

G-3.4: Apply properties of isosceles and equilateral triangles to solve problems.

Classifying Triangles
Concurrent Lines, Medians, and Altitudes
Isosceles and Equilateral Triangles
Triangle Inequalities

G-3.5: Use interior angles, exterior angles, medians, angle bisectors, altitudes, and perpendicular bisectors to solve problems.

Concurrent Lines, Medians, and Altitudes
Segment and Angle Bisectors
Similarity in Right Triangles
Triangle Angle Sum

G-3.6: Apply the triangle sum theorem to solve problems.

Isosceles and Equilateral Triangles
Polygon Angle Sum
Triangle Angle Sum

G-3.7: Apply the triangle inequality theorem to solve problems.

Triangle Inequalities

G-3.8: Apply congruence and similarity relationships among triangles to solve problems.

Congruence in Right Triangles
Constructing Congruent Segments and Angles
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures
Similarity in Right Triangles

G-3.9: Apply theorems to prove that triangles are either similar or congruent.

Congruence in Right Triangles
Proving Triangles Congruent
Similar Figures

G-3.10: Use the Pythagorean theorem and its converse to solve problems.

Circles
Cosine Function
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Sine Function
Surface and Lateral Areas of Pyramids and Cones
Tangent Function

G-3.11: Use the properties of 45-45-90 and 30-60-90 triangles to solve problems.

Cosine Function
Sine Function
Tangent Function

G-3.12: Use trigonometric ratios (including sine, cosine, and tangent) to solve problems involving right triangles.

Cosine Function
Sine Function
Sine, Cosine, and Tangent Ratios
Tangent Function

G-4: The student will demonstrate through the mathematical processes an understanding of the properties of quadrilaterals and other polygons and the relationships between and among them.

G-4.1: Carry out a procedure to compute the perimeter of quadrilaterals, regular polygons, and composite figures.

Perimeter and Area of Rectangles
Perimeters and Areas of Similar Figures

G-4.2: Carry out a procedure to find the area of quadrilaterals, regular polygons, and composite figures.

Area of Parallelograms
Area of Triangles
Perimeter and Area of Rectangles
Perimeters and Areas of Similar Figures

G-4.3: Apply procedures to compute measures of interior and exterior angles of polygons.

Polygon Angle Sum
Triangle Angle Sum

G-4.4: Analyze how changes in dimensions affect the perimeter or area of quadrilaterals and regular polygons.

Perimeter and Area of Rectangles

G-4.5: Apply the properties and attributes of quadrilaterals and regular polygons and their component parts to solve problems.

Classifying Quadrilaterals
Parallelogram Conditions
Special Parallelograms

G-4.6: Apply congruence and similarity relationships among shapes (including quadrilaterals and polygons) to solve problems.

Constructing Congruent Segments and Angles
Parallelogram Conditions
Perimeters and Areas of Similar Figures
Similarity in Right Triangles

G-5: The student will demonstrate through the mathematical processes an understanding of the properties of circles, the lines that intersect them, and the use of their special segments.

G-5.1: Carry out a procedure to compute the circumference of circles.

Circumference and Area of Circles

G-5.2: Carry out a procedure to compute the area of circles.

Circumference and Area of Circles

G-5.4: Carry out a procedure to compute the length of an arc or the area of a sector of a circle.

Inscribed Angles

G-5.5: Apply the properties of the component parts of a circle (including radii, diameters, chords, sectors, arcs, and segments) to solve problems.

Chords and Arcs
Circles
Inscribed Angles

G-5.7: Apply the properties of central angles, inscribed angles, and arcs of circles to solve problems.

Chords and Arcs
Inscribed Angles

G-6: The student will demonstrate through the mathematical processes an understanding of transformations, coordinate geometry, and vectors.

G-6.1: Use the distance formula to solve problems.

Circles
Distance Formula

G-6.2: Use the midpoint formula to solve problems.

Circles

G-6.3: Apply transformations?translation, reflection, rotation, and dilation?to figures in the coordinate plane by using sketches and coordinates.

Dilations
Rotations, Reflections, and Translations
Translations

G-6.4: Apply transformations (including translation and dilation) to figures in the coordinate plane by using matrices.

Dilations
Translations

G-6.5: Carry out a procedure to represent the sum of two vectors geometrically by using the parallelogram method.

Adding Vectors

G-6.6: Carry out a procedure to determine the magnitude and direction of the resultant of two vectors by using a scale drawing and direct measurement.

Adding Vectors
Vectors

G-6.8: Carry out a procedure to determine the direction of the resultant of two perpendicular vectors by using a scale drawing and direct measurement.

Adding Vectors
Vectors

G-7: The student will demonstrate through the mathematical processes an understanding of the surface area and volume of three-dimensional objects.

G-7.1: Carry out a procedure to compute the surface area of three-dimensional objects (including cones, cylinders, pyramids, prisms, spheres, and hemispheres).

Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

G-7.2: Carry out a procedure to compute the volume of three-dimensional objects (including cones, cylinders, pyramids, prisms, spheres, hemispheres, and composite objects).

Prisms and Cylinders
Pyramids and Cones

G-7.4: Apply congruence and similarity relationships among geometric objects to solve problems.

Circles
Constructing Congruent Segments and Angles
Perimeters and Areas of Similar Figures

G-7.5: Apply a procedure to draw a top view, front view, and side view of a three-dimensional object.

3D and Orthographic Views

G-7.6: Apply a procedure to draw an isometric view of a three-dimensional object.

3D and Orthographic Views