per session

Mastering High School Geometry: From Basics to Proofs

Ages 14-18

Live 1-on-1 Lessons

The class guides students through key topics such as proofs, similarity and congruence, circles, transformations, trigonometry, and more. Ideal for those aiming to boost their grades, gain confidence, and excel in exams.

Yosef

Live video meetings

Meets 3x per week (teacher suggestion)

Meets on demand

55 min

About Learning Overview Teacher Reviews

What's included

Meets on Demand

schedule meetings as needed

55 mins

per session

Teacher support

Homework

1-2 hours per week. included

Class Experience

US Grade 8 - 12

My class, "Mastering High School Geometry: From Basics to Proofs," is designed to help students master the fundamental concepts of geometry. We will cover a wide range of topics, from basic shapes and angles to more advanced topics like proofs and transformations.
Geometry Tutoring Syllabus

Course Duration: 12 Weeks
Objective: Develop a strong foundation in geometric concepts, logical reasoning, and problem-solving skills.

Week 1: Basics of Geometry

. Points, lines, planes, and angles
. Types of angles (acute, right, obtuse, straight)
. Measuring and classifying angles
. Segment and angle bisectors
. Midpoints and distance formula

Week 2: Reasoning and Proofs

. Inductive vs. deductive reasoning
. Conditional statements and their converses
. Properties of equality and congruence
. Writing two-column proofs and paragraph proofs

Week 3: Parallel and Perpendicular Lines

. Properties of parallel lines and transversals
. Identifying corresponding, alternate interior, and same-side interior angles
. Slope and equations of parallel and perpendicular lines
. Proving lines are parallel or perpendicular

Week 4: Transformations

. Reflections, translations, rotations, and dilations
. Properties of rigid and non-rigid transformations
. Compositions of transformations
. Symmetry (line and rotational)

Week 5: Congruent Triangles

. Triangle congruence criteria (SSS, SAS, ASA, AAS, HL)
. Using congruence to prove parts of triangles are congruent
. Isosceles and equilateral triangle properties
. Overlapping triangles in proofs

Week 6: Relationships Within Triangles

. Midsegments and their properties
. Perpendicular bisectors, angle bisectors, medians, and altitudes
. Triangle inequalities
. Hinge Theorem
Week 7: Quadrilaterals and Other Polygons

. Properties of parallelograms, rectangles, rhombuses, squares, and trapezoids
. Conditions for proving quadrilateral types
. Sum of interior and exterior angles in polygons

Week 8: Similarity

. Proportions and similarity ratios
. Triangle similarity (AA, SSS, SAS)
. Proportional parts in triangles
. Using similarity to find missing lengths

Week 9: Right Triangles and Trigonometry

. Pythagorean Theorem and its applications
. Special right triangles (30°-60°-90° and 45°-45°-90°)
. Trigonometric ratios (sine, cosine, tangent)
. Solving right triangles using trig functions

Week 10: Circles

. Parts of a circle (radius, chord, diameter, tangent, secant)
. Arc measures and central angles
. Inscribed angles and their properties
. Equations of circles in coordinate geometry

Week 11: Circumference and Area

. Circumference and arc length
. Area of circles and sectors
. Area of composite figures

Week 12: Surface Area and Volume

. Surface area and volume of prisms, cylinders, pyramids, cones, and spheres
. Applying the formulas to real-world problems
. Effects of changing dimensions on surface area and volume

Learning Goals

Understand and apply the principles of geometric transformations, such as translations, rotations, reflections, and dilations.
Develop the ability to write and understand geometric proofs, including two-column proofs and paragraph proofs.

Other Details

External Resources

Learners will not need to use any apps or websites beyond the standard Outschool tools.

Meet the teacher

Yosef

Joined March, 2025

Profile

Teacher expertise and credentials

Bachelor's Degree in Civil Engineering from Portland State University

I have been tutoring math for over two decades, working with students at all levels, from elementary school to college. As a civil engineer with a strong foundation in geometry and a passion for teaching, I enjoy helping students develop a deep understanding of mathematical concepts and problem-solving techniques. Throughout my career, I have worked extensively with high school students on mastering geometry, both in one-on-one sessions and in classroom-style tutoring.

I have taught high school geometry in various settings, including private tutoring, group sessions, and SAT/ACT preparation courses. My instruction covers essential topics such as parallel lines and transversals, triangle congruence and similarity, properties of polygons, circles, coordinate geometry, transformations, and proof-based reasoning. I emphasize logical thinking and visualization, helping students build confidence in their ability to analyze and solve geometric problems.

I have worked with children and teens in various educational settings, supporting public school, private school, and homeschool students. My experience enables me to adapt my teaching strategies to meet individual learning needs, whether students are struggling with geometry fundamentals or seeking to master advanced topics. I am committed to helping students succeed by making geometry engaging, accessible, and enjoyable.