Geometry is the branch of mathematics that deals with the study of shapes, sizes, and properties of spaces. It is an important subject that is used in various fields such as engineering, architecture, and design.

Some of the basic concepts in geometry include:

**Points:**Represented by a dot and has no size**Lines:**Straight path that goes on indefinitely in both directions**Angles:**Formed by two rays with a common endpoint**Shapes:**Two-dimensional (2D) and three-dimensional (3D) objects such as squares, circles, cubes, and spheres

Some key formulas in geometry include:

**Area of a Rectangle:**A = length x width**Area of a Triangle:**A = 1/2 x base x height**Area of a Circle:**A = πr^{2}**Volume of a Cube:**V = side x side x side**Volume of a Cylinder:**V = πr^{2}h

There are several types of angles in geometry, including:

**Acute Angle:**An angle that measures less than 90 degrees**Obtuse Angle:**An angle that measures more than 90 degrees but less than 180 degrees**Right Angle:**An angle that measures exactly 90 degrees**Straight Angle:**An angle that measures exactly 180 degrees

Some key theorems in geometry include:

**Pythagorean Theorem:**In a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides: a^{2}+ b^{2}= c^{2}**Triangle Sum Theorem:**The sum of the interior angles of a triangle is always 180 degrees**Circle Theorems:**Various theorems related to angles and arcs in a circle

Geometry is a fundamental branch of mathematics that plays a crucial role in understanding the world around us. By mastering the basic concepts, formulas, and theorems in geometry, you will be able to solve a wide range of problems and apply geometric principles in real-world situations.

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Algebra (NCTM)

Represent and analyze mathematical situations and structures using algebraic symbols.

Develop an initial conceptual understanding of different uses of variables.

Use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships.

Recognize and generate equivalent forms for simple algebraic expressions and solve linear equations

Grade 7 Curriculum Focal Points (NCTM)

Number and Operations and Algebra: Developing an understanding of operations on all rational numbers and solving linear equations

Students extend understandings of addition, subtraction, multiplication, and division, together with their properties, to all rational numbers, including negative integers. By applying properties of arithmetic and considering negative numbers in everyday contexts (e.g., situations of owing money or measuring elevations above and below sea level), students explain why the rules for adding, subtracting, multiplying, and dividing with negative numbers make sense. They use the arithmetic of rational numbers as they formulate and solve linear equations in one variable and use these equations to solve problems. Students make strategic choices of procedures to solve linear equations in one variable and implement them efficiently, understanding that when they use the properties of equality to express an equation in a new way, solutions that they obtain for the new equation also solve the original equation.