About the Course
CORE COURSE
This course focuses on foundations of geometry and trigonometry on the high school level. Where possible, problems from Chumash and Tanach are brought up in the context of topics studied. Visually appealing, this course brings up topics of sacred geometry and studies its aspects within Torah context.
First Semester:
Geometry Focus
Unit 1: Basics of Geometry (3-4 weeks)
Topics Covered:
Points, lines, planes, and angles.
Segment and angle bisectors.
Complementary, supplementary, vertical, and adjacent angles.
Introduction to deductive reasoning and basic proofs.
Objectives:
Understand foundational geometric terms.
Develop skills in reasoning and constructing simple geometric proofs.
Unit 2: Parallel and Perpendicular Lines (3-4 weeks)
Topics Covered:
Properties of parallel and perpendicular lines.
Angle relationships with parallel lines and transversals.
Proving lines are parallel or perpendicular.
Slopes of parallel and perpendicular lines.
Objectives:
Apply properties of parallel lines to solve geometric problems.
Use algebraic and geometric methods to prove relationships between lines.
Unit 3: Triangle Congruence and Properties (4-5 weeks)
Topics Covered:
Triangle classification and properties.
Triangle congruence criteria (SSS, SAS, ASA, AAS, HL).
Isosceles and equilateral triangles.
Proving triangle congruence and applying it to problem-solving.
Objectives:
Master triangle congruence postulates.
Develop proof-writing skills with triangles.
Unit 4: Polygons and Quadrilaterals (3-4 weeks)
Topics Covered:
Properties and classification of polygons.
Properties of parallelograms, trapezoids, and kites.
Proving quadrilaterals are parallelograms.
Angle sums in polygons.
Objectives:
Understand the properties of different types of polygons and quadrilaterals.
Apply properties of quadrilaterals to solve geometric problems.
Unit 5: Similarity (3-4 weeks)
Topics Covered:
Ratios and proportions in geometry.
Properties of similar triangles.
Proving triangle similarity (AA, SSS, SAS).
Applications of similarity in the real world.
Objectives:
Solve problems using properties of similar figures.
Prove figures are similar using geometric postulates and theorems.
Second Semester:
Geometry with Trigonometry
Unit 6: Circles (4-5 weeks)
Topics Covered:
Properties of circles, arcs, chords, tangents, and secants.
Angle relationships in circles.
Segment lengths in circles (chord-chord, secant-secant, tangent-secant).
Objectives:
Understand key properties of circles and solve related geometric problems.
Apply circle theorems to prove statements and solve real-world problems.
Unit 7: Area and Volume (4-5 weeks)
Topics Covered:
Area of polygons and circles.
Surface area and volume of 3D figures: prisms, cylinders, pyramids, and spheres.
Real-world applications of area and volume in design and construction.
Objectives:
Solve problems related to areas and volumes of various geometric shapes.
Apply geometric formulas in practical contexts such as architecture and engineering.
Unit 8: Introduction to Trigonometry (4-5 weeks)
Topics Covered:
The Pythagorean theorem and its applications in geometry.
Introduction to trigonometric ratios: sine, cosine, tangent.
Solving right triangles using trigonometry.
Real-world applications of trigonometry in navigation, physics, and architecture.
Objectives:
Use trigonometric ratios to solve problems involving right triangles.
Understand how trigonometry is applied in various real-world contexts.
Unit 9: Geometric Proofs, Trigonometric Applications, and Review (3-4 weeks)
Topics Covered:
Review of key geometric concepts and proof techniques.
Advanced geometric proofs incorporating trigonometry.
Applications of geometry and trigonometry in real-world problem-solving.
Objectives:
Reinforce and synthesize geometry and trigonometry concepts through project-based learning.
Solve complex problems requiring the integration of geometry and trigonometry.