• Course Description

Geometry provides an analysis of plane, solid, and coordinate geometry. Points, lines and planes form the foundations of geometry. From this foundation we use inductive and deductive reasoning to make conclusions. Students explore both abstract mathematical concepts as well as real-world applications. Technological tools and manipulatives will be used to discover and explore more complex geometric situations. This allows students to deepen their understanding of geometric relationships as they move toward formal mathematical arguments.  As students encounter challenging problems, and practice asking for help and a willingness to learn from others, they build the social emotional learning competencies of self-management, self awareness, relationship skills, and social awareness.

Related Priority Standards (State &/or National): K-12 Mathematics Missouri Learning Standards

Essential Questions:

• How do you logically think through problems?
• How can geometric properties be used to prove relationships between lines and angles?
• Why is it important to prove every logical step in a proof?
• Why might there be more than one correct way to write a proof?
• How do you recognize symmetry in a figure?
• How will knowing the formulas for area and perimeter help in your daily life?
• What is the Golden Ratio and how does it fit into your daily life?
• What is the relationship between area and volume?

Enduring Understanding, Goals, & Objectives

• Students will use the Pythagorean Theorem.
• Students will write logical statements.
• Students will find missing angles and lengths from a diagram.
• Students will construct geometric figures.
• Students will prove theorems.
• Students will calculate volume and surface area of prisms, spheres, pyramids, cones, and cylinders.

Course Level Scope & Sequence (Units &/or Skills):

Intro Unit: Reasoning in Geometry

• Students will use the Pythagorean Theorem.
• Students will write logical statements.
• Students will use inductive and deductive reasoning to make predictions.

Unit 1: Foundations in Geometry

• Students will sketch accurate diagrams.
• Students will find missing angles and lengths from a diagram.
• Students will construct geometric figures.
• Students will use geometric relationships to set up and solve equations.
• Students will apply geometry relationships to coordinate geometry.

Unit 2: Deductive Reasoning

• Students will find missing angles and lengths from a diagram.
• Students will construct geometric figures.
• Students will use geometric relationships to set up and solve equations.
• Students will apply geometry relationships to coordinate geometry.
• Students will prove theorems.

Unit 3: Rigid Motions

• Students will write a rule for a rigid motion.
• Students will identify symmetries.
• Students will perform rigid motions (translation, reflection, rotation, composition).
• Students will apply inverse transformations.

Unit 4: Congruent Triangles

• Students will find missing angles and lengths from a diagram (simple).
• Students will construct geometric figures.
• Students will use geometric relationships to set up and solve equations.
• Students will prove triangles congruent.
• Students will prove parts of triangles congruent.
• Students will extend parts proofs.
• Students will find the interior and exterior angles of polygons.
• Students will prove and use theorems about triangles.
• Students will classify triangles by sides and by angles.
• Students will find interior and exterior angle measures of triangles.
• Students will use rigid motion to show that two triangles are congruent.
• Students will identify corresponding parts of congruent polygons.
• Students will use rigid motions to prove the SAS Congruence Theorem.
• Students will prove and use theorems about equilateral triangles.
• Students will use rigid motions to prove the SSS Congruence Theorem.
• Students will use rigid motions to prove the AAS Congruence Theorem.
• Students will use congruent triangles to prove statements.
• Students will palace figures in a coordinate plane.

• Students will prove properties of parallelograms.
• Students will solve problems involving parallelograms in the coordinate plane.
• Students will prove that a quadrilateral is a parallelogram.
• Students will find missing lengths that make a quadrilateral a parallelogram.
• Students will show that a quadrilateral in the coordinate plane is a parallelogram.
• Students will identify special quadrilaterals.
• Students will explain how special parallelograms are related.
• Students will identify trapezoids and kites.
• Students will use properties of trapezoids and kites to solve problems.

Unit 6: Area

• Students will apply area and perimeter formulas for rectangles
• Students will apply area and perimeter formulas for triangles
• Students will apply area and perimeter formulas for trapezoids and parallelograms
• Students will apply area and perimeter formulas for circles
• Students will calculate sector area and arc length
• Students will maximize area of quadrilaterals
• Students will calculate area and perimeter of irregular shapes

Unit 7: Similarity

• Students will apply concepts to a new situation.
• Students will justify with reasoning.
• ​​Students will solve proportions.
• Students will find the ratios of perimeter and area of two similar figures.
• Students will use geometric relationships to set up and solve proportions.
• Students will identify similar triangles.
• Students will perform dilations.
• Students will find corresponding lengths in similar polygons.
• Students will determine whether polygons are similar.
• Students will use angle measures of triangles to determine whether triangles are similar.

Unit 8: Trigonometry

• Students will justify with reasoning.
• Students will find sine, cosine, and tangent.
• Students will use the Law of Sines and Law of Cosines to find missing sides and angles.
• Students will use SOH CAH TOA to find missing sides and angles.
• Students will use SOH CAH TOA in a word problem.
• Students will find side lengths in 40-45-90 triangles.
• Students will find side lengths in 30-60-90 triangles.
• Students will use special right triangles to solve real-world problems.
• Students will solve real-life problems by solving right triangles.

Unit 9: Circles

• Students will apply concepts to a new situation.
• Students will justify with reasoning.
• Students will construct geometric figures.
• Students will calculate sector area and arc length.
• Students will find the measurements of arcs, central angles, and inscribed angles.
• Students will apply tangent relationships to find lengths.
• ​​Students will apply the relationship between chords perpendicular to a radius to find angles, arcs, and lengths.
• Students will apply relationships between secants and tangents to find angles and lengths.
• Students will graph a circle given an equation.
• Students will use the formula for the circumference of a circle to find measures.
• Students will find arc lengths and use arc lengths to find measures.
• Students will solve real-life problems involving circumference.
• Students will find areas of sectors of circles.
• Students will solve problems involving areas of sectors.

Unit 10: Volume and Surface Area

• Students will calculate the volume and surface area of prisms.
• Students will calculate the volume and surface area of spheres.
• Students will calculate the volume and surface area of pyramids.
• Students will calculate the volume and surface area of cylinders.
• Students will calculate the volume and surface area of cones.
• Students will calculate volume and surface area of irregular shapes.
• Students will find the ratios of volume of two similar solids.

Course Resources & Materials:   Math Medic, Delta Math

Date Last Revised/Approved: April 2023