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What is Geometry?

Geometry is a math course that is used to study the properties and relationships of shapes, sizes, positions, and dimensions of objects. Geometry concepts are used for designing buildings, bridges, and other structures. Apart from this, they are also used in making computer graphics and animations for movies & video games, and much more. You’ll learn the following topics in geometry:

Coordinate planes

In coordinate planes, students will learn how to plot points on the coordinate plane, identify the coordinates of points, and graph equations in plane geometry. They will also learn about the distance formula, which is used to find the distance between two points on the coordinate plane, and the midpoint formula, which is used to find the midpoint between two points on the coordinate plane.

With these geometry skills, students will be able to represent geometric figures, such as lines and circles, in a graphical form and write geometry equations. They will be able to analyze and interpret graphical data, and use the coordinate plane to solve real-world problems and apply them in real-world applications. For example, students may use the coordinate plane to represent data from a survey, analyze the trend of a stock market, or determine the location of a treasure in a treasure hunt.

Pythagoras theorem

Pythagoras theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. With this concept, students will learn how to identify right triangles and apply the theorem to find the missing side lengths. They will also learn how to use the Pythagorean theorem to apply in real-world applications and solve real-world problems involving distance and measurement, such as finding the distance between two points on a map or the height of a building.

After all this knowledge, they will have a better understanding of the properties of right triangles with right angles and be able to apply the theorem to find missing side lengths or distances.

Triangles (Types, angles, and inequality theorem)

In triangles (types, angles, and inequality theorem), students will learn about various types such as scalene, isosceles, equilateral, acute, obtuse, and right-angled triangles and how to calculate the perimeter, area, and height of these triangles. They will also learn about the different types of angles that can be formed within a triangle, including acute, obtuse, exterior, interior, and right angles, how to write them in geometry equations, and how to measure and calculate these angles using different methods such as the angle sum property of triangles and the exterior angle theorem. 

Students will also learn about the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side, and learn to use this theorem to determine if three given sides can form a triangle or not.

After gaining this knowledge, they will be able to identify and classify different types of triangles, determine their properties, and solve problems related to triangles using various theorems and formulas.

Shapes (Properties and classifications)

In shapes (Properties and classifications), students will learn about various shapes, such as squares, rectangles, circles, triangles, and polygons, their properties, classifications, and characteristics, including the number of sides, angles, and vertices. They will also learn how to classify shapes based on their properties and apply this knowledge to solve problems. For example, they may be asked to identify shapes that are congruent or similar or determine the perimeter and area of various shapes.

After gaining this knowledge, they will be able to analyze the properties of different shapes and use this knowledge to solve real-world problems. For example, they may apply their knowledge of the properties of shapes to design a building or layout a garden.

Angles and their types

In angles and their types, students will learn about complementary and supplementary angles, exterior and interior angles of polygons, and how to calculate their measures. They will also learn about acute, right, obtuse, and straight angles, how to identify them in different figures, about angle bisectors, and how they divide an angle into two congruent angles.

In the end, they will be able to identify different types of angles and understand their properties. They will also be able to measure and compare angles, and solve problems involving angles in different shapes and figures.

Volume & Surface area

In volume & surface area, students will learn about the volume and surface area of various 3D objects, including prisms, cylinders, cones, and spheres and how to calculate the volume and surface area of these shapes using various formulas. They will also learn how to visualize and manipulate these shapes in their minds.

After this knowledge, students will be able to calculate the volume and surface area of various 3D objects, understand the relationships between different shapes and their dimensions, and apply these skills to solve real-world problems related to geometry and measurement.

Heron’s formula

In geometry, Heron’s formula is used to find the area of a triangle given the lengths of its three sides. Heron’s formula states that the area of a triangle whose sides have lengths a, b, and c is given by the formula: 

Area = square root of (s(s-a)(s-b)(s-c)) 

where, s = (a+b+c)/2 is the semi-perimeter of the triangle.

Students will learn to apply this formula to solve problems related to finding the area of a triangle.

With these geometry skills, students will be able to identify when to use Heron’s formula and when to use other methods to find the area of a triangle. They will also be able to write them in geometry equations, explain the derivation of the formula and apply it to real-world problems, such as calculating the area of a triangular garden or the area of a triangular sail on a boat.

Area & Perimeter

In area & perimeter, students will learn how to find the area and perimeter of basic shapes like squares, rectangles, and triangles. As they progress, they learn about more complex shapes such as circles, trapezoids, and polygons, and how to find their area and perimeter using a combination of formulas and techniques.

They will also learn how to apply this concept to real-world problems. For example, they may need to find the area of a room to determine how much paint or carpet is needed.

After gaining this knowledge, they will be able to accurately calculate the area and perimeter of a wide variety of shapes, and apply these geometry skills to solve real-world problems, like finding the perimeter of a property to determine how much fencing is required.

Similarity of triangles

In similarity of triangles, students will learn that two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are proportional and also learn the various methods to write them in geometry equations and prove the similarity of triangles such as Angle-Angle (AA), Side-Angle-Side (SAS), and Side-Side-Side (SSS) similarity criteria. 

After all this knowledge, they will be able to find the ratio of the corresponding sides of similar triangles, which is known as the scale factor. They will also be able to apply this concept to solve real-world problems involving similar triangles, such as finding the height of a building or determining the distance between two points using indirect measurement techniques.

What are the benefits of learning geometry?

Learning geometry has many benefits, such as:

1. Spatial reasoning: Geometry helps develop spatial reasoning, which is the ability to visualize and manipulate objects in one’s mind. This skill is useful in fields such as engineering, architecture, and design.

2. Problem-solving: Geometry involves logical reasoning and problem-solving skills. By solving geometric problems, students develop critical thinking skills that are transferable to other areas of life.

3. Visual thinking: Geometry is a visual subject that requires students to understand and create diagrams, graphs, and models. This enhances their ability to think visually and communicate ideas effectively.

4. Mathematical skills: Geometry involves algebraic thinking, measurement, and numerical reasoning. By studying plane geometry, students improve their math skills and develop a deeper understanding of mathematical concepts.

5. Cultural appreciation: Geometry has a rich history and cultural significance, with contributions from ancient cultures such as the Greeks and Egyptians. By studying geometry, students gain an appreciation for the cultural significance of mathematics and its role in human history.

Overall, learning geometry can help you in gaining practical skills that can be applied to a variety of careers.

How can you benefit from a Wiingy online Geometry tutor?

Wiingy’s geometry tutors can provide you with many benefits, such as:

1. Flexibility: You can learn at your own pace and on your own schedule. This allows you to fit your learning around your other works.

2. Expert guidance: The Geometry online tutoring from Wiingy is designed and led by experienced geometry teachers who can provide you with guidance and support.

3. Interactive learning: The sessions use a variety of interactive tools and activities to help you engage with the material and retain what you learn.

4. Personalized learning: The Geometry online tutoring sessions from Wiingy can adapt to your individual learning style and pace, providing you with a personalized learning experience.

5. Affordable: Wiingy’s Geometry online tutoring sessions are more affordable than traditional in-person tutoring or courses, making it a cost-effective option for learning geometry.