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Understand equations, functions, and problem-solving

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Aligned with Common Core and state standards requirements

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Geometry Topics

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Measuring Systems
Conversions between metric and imperial systems
Metric systems in measuring systems
Imperial systems in measuring systems
Conversions involves squares and cubes
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Surface Area and Volume
Surface area and volume of prisms
Surface area and volume of cones
Surface area and volume of spheres
Surface area and volume of cylinders
Surface area and volume of pyramids
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Points, Lines, Segments, Midpoints and Chords
Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)M=(2x1​+x2​​,2y1​+y2​​)
Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}d=(x2​−x1​)2+(y2​−y1​)2​
Slope-Y-intercept form: y = mx + b
Graph using a single point and slope
Solve linear equations
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Circles, plane and coordinate
Circles and circumference
Arcs of a circle
Areas and sectors of circles
Angles in a circle
Chord properties in circle geometry
Tangent properties in circle geometry
Central angles and proofs
Inscribed angles and proofs
Central and inscribed angles in circles
Circle chord, tangent, and inscribed angles proofs
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Triangles and special triangles
Pythagorean theorem
Solving expressions using 45-45-90 special right triangles
Solving expressions using 30-60-90 special right triangles
Classifying triangles
Congruence and congruent triangles
Triangles congruent by SSS proofs
Triangles congruent by SAS and HL proofs
Triangles congruent by ASA and AAS proofs
Isosceles and equilateral triangles
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Angles and trigonometry
Use sine ratio to calculate angels and side (Sin = oh)\frac{o}{h})ho​)
Use cosine ratio to calculate angles and side (Cos = ah \frac{a}{h}ha​ )
Use tangent ratio to calculate angles and side (Tan = oa \frac{o}{a}ao​ )
Combination of SohCahToa questions
Word problems relating ladder in trigonometry
Word problems relating guy wire in trigonometry
Other word problems relating angles in trigonometry
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Sine Rule and Cosine Rule
Law of sines
Law of cosines
Applications of the sine law and cosine law
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Bearings
Introduction to bearings
Bearings and direction word problems
Angle of elevation and depression
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Transformations
Line symmetry
Rotation symmetry and transformations
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Similarity
Scale diagrams
Similar triangles
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2D figures and 3D figures
Tessellations using rotations
Surface area of three-dimensional (3D) objects
Nets of three-dimensional objects
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Probability
Probability of independent events
Permutations
Fundamental counting principle
Solve problems involving both permutations and combinations
Probability with Venn diagrams
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Logic
Inductive reasoning
Statements
Negations
Conjunctions and disjunctions
Truth tables
Conditionals
Inverses, converses, and contrapositives
Biconditionals
Deductive reasoning
Algebraic proofs
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Reasoning
Consecutive integers
Number sequences
Finding the missing digit
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Set Theory
Set notation
Set builder notation
Intersection and union of 2 sets
Intersection and union of 3 sets
Interval notations
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Vectors
Introduction to vectors
Magnitude of a vector
Direction angle of a vector
Equivalent vectors
Adding and subtracting vectors in component form
Word problems on vectors
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Angles, lines and transversals
Pairs of lines and angles
Parallel lines and transversals
Parallel line proofs
Perpendicular line proofs
Parallel line equations
Parallel and perpendicular lines

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What is Geometry?

Understanding geometry can be difficult. With so many sub-topics under the umbrella of Geometry it can be difficult to grasp what exactly is Geometry, why and when could ever be useful? Generally speaking, Geometry is study of shapes – how they can be transformed, scaled, measuring/calculating the angles found within them, as well as other characteristics such as area, volume, and so forth. The study of Geometry also involves the study of lines, the building blocks of shapes, and their properties. Here at StudyPug, Geometry will also introduce you to the realm of statistics where we look at probability, and how this is to shapes (i.e. Venn diagrams).

Who is known as the father of geometry?

The honour and prestige of this title was bestowed to the one and only Euclid of Alexandria. He was an incredible Mathematician who studied at Plato's Academy in Greece and the first to study Geometry. He went on to publish a variety of textbooks used by mathematicians to this day. He is most known for his work on a publication titled "The Elements" that feature ground-breaking content on algebra, number theories, and of course, geometry. It is said that this masterpiece was what earned him the title of "Father of Geometry" (https://en.wikipedia.org/wiki/Euclid).

Is geometry hard?

Studying Geometry can have its challenges and learning curves, but that's why we're here! Here at StudyPug, we offer help for all - those who fall under the category of Geometry for dummies or those who are looking for more practice and/or advanced questions. At StudyPug we strive to make learning geometry easy, accessible, and engaging. With over 1000's of lessons, Step-by-step examples, and 24/7 help, we are prepared to help students with endless opportunities for easy practice, be it for Geometry exam preparation or to simply to reinforce learning. Here at StudyPug we cover a wide variety of questions you may encounter and we also use a variety of Geometry textbooks (e.g. Prentice Hall Geometry; Glencoe Geometry; McDougal Littell Geometry; Big Ideas Math Geometry) to cater comprehensively to the content you may be learning. Rest assured, we're well equipped to help with the fundamental concepts and basic problems that will allow you to progress confidently to more complex, challenging questions at your own pace.

What is Euclidean geometry?

Euclidean geometry is the branch of geometry that is focused on the study of 2-dimension solid geometry and planes. Some examples include basic facts such as the interior angles of triangles should equal to 180 degrees and that the shortest distance between point A and B is a straight line. Euclidean geometry was built on the basis of Euclid mathematical theories and postulates, most notably composed and synthesized in his publication "The Elements". In a broader sense, Euclidean geometry is also referred to the importance of utilizing cognitive abilities in Math. This encompasses the learner to defer techniques of memorization and formulas, and to rely on a strong, holistic understanding of the subject that allows application of skills and techniques to solve Math problems. While you may have begun studying Euclidean geometry early on in school, you will soon begin exploring concepts of non-euclidean geometry (e.g. properties of 3D shapes, such as a sphere).

How to pass geometry?

Whether you're preparing for a Geometry test, exam, or simply require Geometry help, StudyPug is here to help you succeed and pass your assessments through our Geometry tutoring and Geometry lessons. Our Geometry tutors will cover content, study tips, strategies, and practice questions that will provide you with as much help with Geometry as you need. We recommend starting with the difficult sub-topics/chapters you are struggling with, follow our Geometry tutorials as we take you step-by-step through the process of understanding a concept or problem you may have. Some concepts or problems are trickier than others so you may need to revisit theses areas more than once, which shouldn't be a problem given your unlimited, 24/7 access. Once you are feeling confident, we encourage you to practice, practice, practice! This enables you to be prepared for different styles of questions as well as different levels of difficulty. These questions will supplement your learning and truly test your understanding.

What grade is geometry?

Students begin learning Geometry in 10th Grade. Students should have a strong understanding of Algebra 1 (completed in 9th Grade) before beginning to tackle topics covered in Geometry. For a refresher, please see our Algebra 1 page. Following the completion of Geometry, students may proceed to beginning Algebra 2. Ahead of the game? Wonder what comes after Geometry? Visit our Algebra 2 page for more learning.

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