Geometry

Coming in 2023/2024

Points, Lines, Planes, and Angles

We will learn about lines, planes, and angles and how they can be used to prove theorems.

  • Points, Lines, and Planes
  • Linear Measure and Precision
  • Distance and Midpoints
  • Angle Measure
  • Angle Relationships
  • Polygons
Reasoning and Proof

We will learn about logic and reasoning used throughout geometry to solve problems and reach conclusions.

  • Inductive Reasoning and Conjecture
  • Logic
  • Conditional Statements
  • Deductive Reasoning
  • Postulates and Paragraph Proofs
  • Algebraic Proof
  • Proving Segment Relationships
  • Proving Angle Relationships
Parallel and Perpendicular Lines

We will identify angle relationships that occur with parallel lines and a transversal and identify and prove lines parallel from given angle relationships.

  • Parallel Lines and Transversals
  • Angles and Parallel Lines
  • Slopes of Lines
  • Equations of Lines
  • Proving Lines Parallel
  • Perpendiculars and Distance
Congruent Triangles

We will classify triangles and identify corresponding parts of congruent triangles. We will also apply the Angle Sum Theorem and the Exterior Angle Theorem and use properties of isosceles and equilateral triangles.

  • Classifying Triangles
  • Angles of Triangles
  • Congruent Triangles
  • Proving Congruence – SSS, SAS
  • Proving Congruence – ASA, AAS
  • Isosceles Triangles
  • Triangles and Coordinate Proof
Relationships in Triangles

We will identify and use perpendicular bisectors, angle bisectors, medians, and altitudes of triangles. We will also apply properties of inequalities relating to the measures of angles and sides of triangles.

  • Bisectors, Medians, and Altitudes
  • Inequalities and Triangles
  • Indirect Proof
  • The Triangle Inequality
  • Inequalities Involving Two Triangles
Proportions and Similarity

We will identify similar polygons and use ratios and proportions to solve problems. We will also recognize and use proportional parts, corresponding perimeters, altitudes, angle bisectors, and medians of similar triangles to solve problems.

  • Proportions
  • Similar Polygons
  • Similar Triangles
  • Parallel Lines and Proportional Parts
  • Parts of Similar Triangles
  • Fractals and Self-Similarity
Right Triangles and Trigonometry

We will solve problems using the geometric mean, the Pythagorean Theorem, and its converse. We will also use trigonometric ratios to solve right triangle problems.

  • Geometric Mean
  • The Pythagorean Theorem and Its Converse
  • Special Right Triangles
  • Trigonometry
  • Angles of Elevation and Depression
  • The Law of Sines
  • The Law of Cosines
Quadrilaterals

We will investigate the interior and exterior angles of polygons and recognize and apply the properties of parallelograms. We will also recognize and apply the properties of rectangles, rhombi, squares, and trapezoids.

  • Angles of Polygons
  • Parallelograms
  • Tests for Parallelograms
  • Rectangles
  • Rhombi and Squares
  • Trapezoids
  • Coordinate Proof with Quadrilaterals
Transformations

We will recognize figures that have been reflected, translated, rotated, or dilated. We will also find the magnitude and direction of vectors and perform operations on vectors.

  • Reflections
  • Translations
  • Rotations
  • Tessellations
  • Dilations
  • Vectors
  • Transformations with Matrices
Circles

We will identify parts of a circle and solve problems involving circumference. We will also find measures of angles and segments in a circle and write the equation of a circle.

  • Circles and Circumference
  • Angles and Arcs
  • Arcs and Chords
  • Inscribed Angles
  • Tangents
  • Secants, Tangents, and Angle Measures
  • Special Segments in a Circle
  • Equations of Circles
Areas of Polygons and Circles

We will find areas of parallelograms, triangles, rhombi, trapezoids, regular polygons, and circles. We will also find geometric probability and areas of sectors and segments of circles.

  • Areas of Parallelograms
  • Areas of Triangles, Trapezoids, and Rhombi
  • Areas of Regular Polygons and Circles
  • Areas of Irregular Figures
  • Geometric Probability
Surface Area

We will find the lateral areas and surface areas of prisms, cylinders, pyramids, and cones. We will also find the surface areas of spheres and hemispheres.

  • Three-Dimensional Figures
  • Nets and Surface Area
  • Surface Areas of Prisms
  • Surface Areas of Cylinders
  • Surface Areas of Pyramids
  • Surface Areas of Cones
  • Surface Areas of Spheres
Volume

We will find volumes of prisms, cylinders, pyramids, cones, and spheres. We will also identify congruent and similar solids and state their properties.

  • Volumes of Prisms and Cylinders
  • Volumes of Pyramids and Cones
  • Volumes of Spheres
  • Congruent and Similar Solids
  • Coordinates in Space