Geometry

A Contemplanda online course.

Geometry begins with points, lines, and planes, the measurement of segments and angles, basic constructions, and reasoning and proof. It then treats rigid transformations and congruence, and similarity with right-triangle trigonometry, and the first semester ends with parallel and perpendicular lines and the relationships within triangles. The second semester covers quadrilaterals and other polygons, circles, and the formulas for circumference, area, and volume, and it closes with a unit on geometric probability.

Most problems ask for a numerical answer or are multiple choice. Others are answered with an expression, an equation solved one step per line, or points placed on the coordinate plane. A few are two-column proofs whose statements are given, and the student chooses the reason that justifies each one. Most problems carry hints, revealed one at a time, and rotatable 3D figures accompany the lessons on solids.

Course at a glance

Course title: Geometry
Publisher: Contemplanda
Structure: 9 units over two semesters
Lessons: 61 lessons
Credit: Not awarded by Contemplanda
Enrollment: Purchasing is not open yet
Course page: www.contemplanda.com/courses/geometry

Credit and enrollment

Contemplanda does not award high school credit. A student who wants credit for the course should ask their own school whether it will accept it.

Purchasing is not open yet. Questions about enrolling can go to info@contemplanda.com.

Students who are already enrolled sign in at direct.contemplanda.com.

Units and lessons

Every published lesson, by semester and unit.

Semester 1

Foundations of geometry

Points, lines, and planes
Segments and distance
Midpoint and distance in the coordinate plane
Angles and angle pairs
Basic constructions
Reasoning and proof

Transformations and congruence

Rigid motions and translations
Reflections
Rotations
Symmetry
Congruent figures
Triangle congruence criteria
Congruence proofs and CPCTC

Similarity and right-triangle trigonometry

Ratios and proportions
Similar polygons and dilations
Proving triangles similar: AA, SAS, and SSS
Parallel lines and proportional parts
Right-triangle similarity and the geometric mean
Sine, cosine, and tangent
Solving right triangles

Parallel and perpendicular lines

Lines and transversals
Parallel lines and transversals
Proving lines parallel
Slopes of parallel and perpendicular lines
Equations of parallel and perpendicular lines
Perpendicular lines and distance
Unit 4 checkpoint

Relationships within triangles

Perpendicular and angle bisectors
The circumcenter and the incenter
Medians and altitudes
The triangle midsegment theorem
Inequalities in one triangle
The hinge theorem
Unit 5 checkpoint

Semester 2

Quadrilaterals and other polygons

Angles of polygons
Parallelograms and their properties
Proving a quadrilateral is a parallelogram
Rectangles, rhombuses, and squares
Trapezoids and kites
Quadrilaterals in the coordinate plane
Unit 6 checkpoint

Circles

Circles and tangents
Arcs, central angles, and chords
Inscribed angles and inscribed polygons
Angles from chords, secants, and tangents
Segment lengths in circles
Circles in the coordinate plane
Unit 7 checkpoint

Circumference, area, and volume

Perimeter and area in the plane
Circumference and arc length
Areas of circles and sectors
Areas of regular polygons
Surface area and volume of prisms and cylinders
Pyramids, cones, and spheres
Unit 8 checkpoint

Geometric probability

What is geometric probability?
Probability with lengths
Probability with angles and spinners
Probability with areas
Probability in the coordinate plane
Unit 9 checkpoint

Assessment

Contemplanda publishes no grade weighting for this course. A school that decides to grant credit for it also decides how the work counts toward a grade.

Academic integrity

Work in the course must be the student's own.

Answer keys for graded questions are never sent to the student's device.

Materials and technology

Where the course runs: In a web browser, through Contemplanda Direct
Textbook: None required. The course's own lessons are the text.