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Geometry for Secondary or High School [Full Course]

Name: Geometry for Secondary or High School [Full Course]
Rating: 4.9 (5 reviews)

A Complete Guide with Fully Worked, Easy-to-Follow Solutions

Created byMathematikos Mathematikos

Last updated 6/2026

English

English [Auto],

What you'll learn

Understand the postulates and axioms about lines, rays, line segments or segments.
Understand the postulates about distance and apply these to triangle inequality concepts.
Understand the concept and postulate of angles in geometry.
Evaluate and prove certain statements mathematically.
Understand the concepts and postulates of a right triangle.
Illustrate the concepts and postulates of angles in a triangle.
Familiarize the coordinate systems.
Write and formulate the equation of the line given points and a slope.
Calculate the distance between points on a line, arbitrary points, higher dimensional space.
Calculate the area of a complex shape triangle and trapezoid.
Apply Pythagoras theorem in calculating and analyzing isosceles and equilateral triangles.
Evaluate and formulate the equation of a circle.
Apply theorems about circles in calculating inscribed angles.
Solve a volume of solid figures.
Analyze and evaluate polygons.
Discuss and apply Euclid's test for congruence.
Evaluate special triangles.
Explain and evaluate similar triangles.
Analyze and solve examination-like problems.
Illustrate and apply the underlying concepts and laws of geometry.

Course content

14 sections • 216 lectures • 11h 33m total length

Introduction1:07

Lines7:15
Practice Exercise 1 [Lines]3:54
Practice Exercise 2 [Lines]2:23
Practice Exercise 3 [Lines]1:21
Relate the distances of three collinear points P, Q, and M by showing PQ plus QM equals PM, establishing the distance relation on a line.
Practice Exercise 4 [Lines]1:55
Distance2:43
Practice Exercise 1 [Distance]6:02
Practice Exercise 2 [Distance]3:11
Practice Exercise 3 [Distance]3:36
Practice Exercise 4 [Distance]3:58
Solve the distance problem from practice exercise four: with XY = 5 units and XZ = 1.5 units, determine ZY as 3.5 units.
Triangle Inequality5:19
Practice Exercise 1 [Triangle Inequality]3:41
Angles7:50
Practice Exercise 1 [Angles]4:01
Practice Exercise 2 [Angles]2:10
Practice Exercise 3 [Angles]2:05
Practice Exercise 4 [Angles]2:36
Practice Exercise 5 [Angles]1:05
Lines and Distance
Lines and Distance
Triangle Inequality
Angles
Angles

Right Angles5:09
Practice Exercise 1 [Right Angles]2:20
Practice Exercise 2 [Right Angles]2:31
Practice Exercise 3 [Right Angles]5:17
Practice Exercise 4 [Right Angles]2:16
Parallel and Opposite Angles4:31
Angles of a Triangle11:53
Practice Exercise 1 [Angles of a Triangle]2:54
Practice Exercise 2 [Angles of a Triangle]3:34
Practice Exercise 3 [Angles of a Triangle]7:16
Practice Exercise 4 [Angles of a Triangle]6:14
Practice Exercise 5 [Angles of a Triangle]3:13
Practice Exercise 6 [Angles of a Triangle]4:21
Practice Exercise 7 [Angles of a Triangle]4:36
Practice Exercise 8 [Angles of a Triangle]5:16
Practice Exercise 9 [Angles of a Triangle]5:00
Practice Exercise 10 [Angles of a Triangle]3:16
Practice Exercise 11 [Angles of a Triangle]3:56
Practice Exercise 12 [Angles of a Triangle]9:16
Practice Exercise 13 [Angles of a Triangle]3:42
Practice Exercise 14 [Angles of a Triangle]2:16
Practice Exercise 15 [Angles of a Triangle]3:12
Practice Exercise 16 [Angles of a Triangle]5:57
Right Angles and Angles of a Triangle
Right Angles and Angles of a Triangle

Coordinate Systems4:12
Practice Exercise 1 [Coordinate Systems]3:52
Practice exercise 1 teaches plotting points on a coordinate system by labeling the x-axis and y-axis, locating the origin, and marking points such as (1,-1), (0,5), (-5,-2), and (1,0).
Practice Exercise 2 [Coordinate Systems]1:04
Practice Exercise 3 [Coordinate Systems]0:58
Practice Exercise 4 [Coordinate Systems]2:42
Practice Exercise 5 [Coordinate Systems]4:24
Practice Exercise 6 [Coordinate Systems]1:18
Equation of a Line4:46
Practice Exercise 1 [Equation of a Line]4:46
Practice Exercise 2 [Equation of a Line]7:40
Practice Exercise 3 [Equation of a Line]6:18
Practice Exercise 4 [Equation of a Line]4:38
Practice Exercise 5 [Equation of a Line]2:28
Practice Exercise 6 [Equation of a Line]3:43
Coordinate Systems
Equation of a Line
Equation of a Line

The Area of a Triangle and Trapezoid5:19
Practice Exercise 1 [The Area of a Triangle and Trapezoid]1:50
Practice Exercise 2 [The Area of a Triangle and Trapezoid]1:11
Practice Exercise 3 [The Area of a Triangle and Trapezoid]1:53
Practice Exercise 4 [The Area of a Triangle and Trapezoid]2:45
Practice Exercise 5 [The Area of a Triangle and Trapezoid]4:06
Practice Exercise 6 [The Area of a Triangle and Trapezoid]3:39
Practice Exercise 7 [The Area of a Triangle and Trapezoid]2:22
Practice Exercise 8 [The Area of a Triangle and Trapezoid]1:11
Practice Exercise 9 [The Area of a Triangle and Trapezoid]1:32
Practice Exercise 10 [The Area of a Triangle and Trapezoid]2:58
Practice Exercise 11 [The Area of a Triangle and Trapezoid]1:25
Practice Exercise 12 [The Area of a Triangle and Trapezoid]2:29
Practice Exercise 13 [The Area of a Triangle and Trapezoid]5:10
Practice Exercise 14 [The Area of a Triangle and Trapezoid]1:48
Practice Exercise 15 [The Area of a Triangle and Trapezoid]3:02
Practice Exercise 16 [The Area of a Triangle and Trapezoid]5:01
Pythagoras Theorem1:59
Practice Exercise 1 [Pythagoras Theorem]2:51
Practice Exercise 2 [Pythagoras Theorem]2:13
Practice Exercise 3 [Pythagoras Theorem]2:08
Practice Exercise 4 [Pythagoras Theorem]3:10
Apply Pythagoras theorem to a cube with equal side lengths to derive its space diagonal. When the side is 2, the diagonal is 2 sqrt(3).
Practice Exercise 5 [Pythagoras Theorem]2:08
Practice Exercise 6 [Pythagoras Theorem]1:59
Practice Exercise 7 [Pythagoras Theorem]3:21
Practice Exercise 8 [Pythagoras Theorem]3:26
Practice Exercise 9 [Pythagoras Theorem]2:22
Practice Exercise 10 [Pythagoras Theorem]2:24
Practice Exercise 11 [Pythagoras Theorem]3:01
Apply the Pythagoras theorem to find the field diagonal from 18 meters and 30 meters, then compute the wire length with 20 meters and that diagonal, yielding about 40 meters.
Practice Exercise 12 [Pythagoras Theorem]3:21
Practice Exercise 13 [Pythagoras Theorem]2:57
Isosceles and Equilateral Triangles2:23
Practice Exercise 1 [Isosceles and Equilateral Triangles]4:12
Practice Exercise 2 [Isosceles and Equilateral Triangles]2:15
Practice Exercise 3 [Isosceles and Equilateral Triangles]6:12
Practice Exercise 4 [Isosceles and Equilateral Triangles]2:09
Practice Exercise 5 [Isosceles and Equilateral Triangles]2:06
Practice Exercise 6 [Isosceles and Equilateral Triangles]2:41
Calculate the side length of an equilateral triangle with a 12-meter perimeter, then use the height from the Pythagorean theorem to compute the area as 2 sqrt(12) square meters.
Practice Exercise 7 [Isosceles and Equilateral Triangles]2:31
Practice Exercise 8 [Isosceles and Equilateral Triangles]2:58
Practice Exercise 9 [Isosceles and Equilateral Triangles]1:13
Practice Exercise 10 [Isosceles and Equilateral Triangles]3:23
Practice Exercise 11 [Isosceles and Equilateral Triangles]2:17
Area of a Triangle
Area of a Trapezoid
Pythagoras
Pythagoras
Isosceles and Equilateral Triangles

Distance Between Points on a Line1:01
Practice Exercise 1 [Distance Between Points on a Line]3:35
Practice Exercise 2 [Distance Between Points on a Line]4:03
Practice Exercise 3 [Distance Between Points on a Line]2:19
Distance Between Arbitrary Points1:41
Practice Exercise 1 [Distance Between Arbitrary Points]3:07
Apply the distance formula to find the distance between points P and Q in two examples, yielding sqrt(106) in both cases.
Practice Exercise 2 [Distance Between Arbitrary Points]3:34
Practice Exercise 3 [Distance Between Arbitrary Points]2:50
Practice Exercise 4 [Distance Between Arbitrary Points]3:47
Practice Exercise 5 [Distance Between Arbitrary Points]3:34
Practice Exercise 6 [Distance Between Arbitrary Points]5:45
Practice Exercise 7 [Distance Between Arbitrary Points]2:56
Practice Exercise 8 [Distance Between Arbitrary Points]5:16
Practice Exercise 9 [Distance Between Arbitrary Points]2:46
Practice Exercise 10 [Distance Between Arbitrary Points]1:44
Higher Dimensional Space2:02
Practice Exercise 1 [Higher Dimensional Space]4:53
Apply the distance formula in three-dimensional space to compute distances between points with triple coordinates, yielding d = sqrt(13) for A and d = 5 sqrt(2) for B.
Practice Exercise 2 [Higher Dimensional Space]4:22
Distance Between Points on a Line
Distance Between Arbitrary Points
Higher Dimensional Space

Circumference of a Circle0:56
Practice Exercise 1 [Circumference of a Circle]1:51
Practice Exercise 2 [Circumference of a Circle]2:00
Practice Exercise 3 [Circumference of a Circle]1:22
Practice Exercise 4 [Circumference of a Circle]1:46
Practice Exercise 5 [Circumference of a Circle]4:13
Practice Exercise 6 [Circumference of a Circle]2:34
Practice Exercise 7 [Circumference of a Circle]0:58
Practice Exercise 8 [Circumference of a Circle]1:44
Practice Exercise 9 [Circumference of a Circle]1:17
Practice Exercise 10 [Circumference of a Circle]1:39
Equation of a Circle1:46
Practice Exercise 1 [Equation of a Circle]2:15
Practice Exercise 2 [Equation of a Circle]2:39
Practice Exercise 3 [Equation of a Circle]6:17
Determine the circle centered at (3,5) with radius 5 using the distance formula, then find the other y-axis intersection (0,9) from the standard equation.
Practice Exercise 4 [Equation of a Circle]2:18
Practice Exercise 5 [Equation of a Circle]2:39
Practice Exercise 6 [Equation of a Circle]2:27
Theorems About Circles5:49
Explore circle theorems: chords, diameters, and tangents. Learn that an inscribed angle equals half its intercepted arc, with three cases, and that a diameter subtends a right angle.
Practice Exercise 1 [Theorems About Circles]0:50
Practice exercise 1 on theorems about circles guides you to find X in diagrams using half-angle reasoning. It includes cases like X equals half of 360 minus 110.
Practice Exercise 2 [Theorems About Circles]1:15
Practice Exercise 3 [Theorems About Circles]1:12
Practice Exercise 4 [Theorems About Circles]0:43
Practice Exercise 5 [Theorems About Circles]2:33
Practice Exercise 6 [Theorems About Circles]1:50
Practice Exercise 7 [Theorems About Circles]3:00
In concentric circles with radii 3 and 7, the tangent chord AB has length 4 sqrt(10), derived from a right triangle with legs 3 and TB and hypotenuse 7.
Practice Exercise 8 [Theorems About Circles]4:48
Practice Exercise 9 [Theorems About Circles]4:19
Practice Exercise 10 [Theorems About Circles]6:06
Circumference of a Circle
Equation of a Circle
Theorems About Circles

Polygons5:26
Practice Exercise 1 [Polygons]0:57
Practice Exercise 2 [Polygons]1:25
Practice Exercise 3 [Polygons]1:55
Apply the formula (s - 2) × 180 ÷ s to find each angle of a regular polygon for A, B, and C with 6, 11, and 14 sides.
Practice Exercise 4 [Polygons]1:56
Practice Exercise 5 [Polygons]1:15
Practice Exercise 6 [Polygons]2:14
Practice Exercise 7 [Polygons]1:04
Practice Exercise 8 [Polygons]1:11
Practice Exercise 9 [Polygons]2:33
Practice Exercise 10 [Polygons]4:58
Practice Exercise 11 [Polygons]2:07
Practice Exercise 12 [Polygons]0:48
Practice Exercise 13 [Polygons]3:43
Practice Exercise 14 [Polygons]1:44
Practice Exercise 15 [Polygons]0:52
Polygons
Polygons

Requirements

Elementary or basic algebra.
Nonetheless, you will learn everything you need to know through solved exercises.

Description

Imagine reading an entire geometry textbook for secondary or high school and solving most of the exercises. Wow—that’s amazing!
Well, that’s exactly what you’ll achieve by enrolling in this course.

This course is based on a comprehensive collection of geometry books. Every topic from these books has been carefully compared, compiled, and discussed, with most of the challenging and essential exercises solved for you.

If you’ve ever wished for more solved examples, this course is perfect for you! While many other courses offer lectures, very few provide an abundance of solved exercises and examples. This course can serve as a supplementary resource or even a primary reference to help you understand geometry at the secondary or high school level. It includes concept overviews and—most importantly—plenty of solved exercises designed to enhance your understanding of concepts, postulates, and axioms in a clear and practical way.

The author’s goal is simple: to teach mathematics through true comprehension. As the world and generations evolve, so must our teaching methods. This is what we call innovation in education. To support this, each concise lecture is followed by numerous examples that apply the discussed mathematical concepts. This ensures that knowledge is transferred effectively by demonstrating how theorems and axioms work in practice.

The author firmly believes that mathematics is a powerful tool for advancement and discovery. Through this innovative approach, these tools are now presented to you. It’s up to the next generation to use them to improve lives and make new discoveries.

Thank you very much, and enjoy learning!

Important Notes:

If you are under 18 years old, please seek advice and guidance from a parent or guardian before enrolling in the course.
Feel free to share this course with your friends, relatives, and family—sharing is caring!

Copyright Notice:
Please do not reproduce this work. You are welcome to use the materials for personal study or classroom lectures. You may also watch the accompanying videos on the YouTube channel. However, reproduction or redistribution in any form is not allowed.
Thank you very much for your understanding.

Who this course is for:

Students who want more and more examples or solved exercises to learn thoroughly the topics in geometry.
Students who want to ace or just pass the examinations.
Supplementary to teachers and lecturers subject materials.
Homeschool or home education.

Geometry for Secondary or High School [Full Course]

What you'll learn

Explore related topics

Course content

Introduction1 lecture • 1min

Lines, Distance and Angles18 lectures • 1hr 5min

Proofs7 lectures • 26min

Right Angles and Angles of a Triangle23 lectures • 1hr 48min

Coordinates14 lectures • 53min

Test 1 (Basic of Geometry for Secondary)0

Area and the Pythagoras Theorem43 lectures • 1hr 59min

The Distance Formula18 lectures • 59min

Circles29 lectures • 1hr 13min

Polygons16 lectures • 34min

Requirements

Description

Who this course is for: