Grade 7
  1. Number System  1.1. Integers  1.1.1. Properties of Integers  1.1.2. Operations on Integers  1.1.3. Additive and Multiplicative Inverses  1.1.4. Applications of Integers  1.2. Rational Numbers  1.2.1. Definition of Rational Numbers  1.2.2. Properties of Rational Numbers  1.2.3. Operations on Rational Numbers  1.2.4. Standard Form of Rational Numbers  1.3. Decimals  1.3.1. Operations on Decimals  1.3.2. Converting Between Fractions and Decimals  1.4. Powers and Exponents  1.4.1. Laws of Exponents  1.4.2. Simplifying Expressions with Exponents  1.4.3. Scientific Notation  1.5. Roots  1.5.1. Square Roots  1.5.2. Cube Roots
  2. Algebra  2.1. Expressions  2.1.1. Algebraic Expressions  2.1.2. Simplifying Expressions  2.1.3. Evaluating Expressions  2.2. Linear Equations  2.2.1. Solving Simple Equations  2.2.2. Applications of Linear Equations  2.3. Algebraic Identities  2.3.1. Expanding Using Identities  2.3.2. Simplifying Using Identities
  3. Ratio and Proportion  3.1. Ratios  3.1.1. Understanding Ratios  3.1.2. Simplifying Ratios  3.1.3. Equivalent Ratios  3.2. Proportion  3.2.1. Concept of Proportion  3.2.2. Direct Proportion  3.2.3. Inverse Proportion  3.3. Unitary Method  3.3.1. Solving Problems Using the Unitary Method
  4. Geometry  4.1. Lines and Angles  4.1.1. Types of Angles  4.1.2. Pairs of Angles  4.1.3. Properties of Parallel Lines and a Transversal  4.1.4. Angle Bisectors  4.2. Triangles  4.2.1. Types of Triangles  4.2.2. Angle Sum Property  4.2.3. Exterior Angle Property  4.2.4. Pythagoras Theorem  4.3. Congruence of Triangles  4.3.1. Criteria for Congruence  4.3.2. Applications of Congruence  4.4. Quadrilaterals  4.4.1. Types of Quadrilaterals  4.4.2. Properties of Parallelograms  4.4.3. Special Quadrilaterals  4.4.4. Properties of Rectangles and Rhombuses
  5. Mensuration  5.1. Perimeter and Area  5.1.1. Perimeter of Plane Figures  5.1.2. Area of Plane Figures  5.1.3. Area of a Trapezium  5.1.4. Area of a Parallelogram  5.1.5. Area of a Circle  5.1.6. Area of Composite Figures  5.2. Surface Area and Volume  5.2.1. Cubes and Cuboids  5.2.2. Surface Area of Cylinders  5.2.3. Volume of Prisms and Cylinders  5.2.4. Volume and Surface Area of Cones
  6. Data Handling  6.1. Data Collection  6.1.1. Organizing Data  6.1.2. Frequency Distribution  6.2. Graphical Representation of Data  6.2.1. Bar Graphs  6.2.2. Double Bar Graphs  6.2.3. Pie Charts  6.2.4. Histograms  6.2.5. Line Graphs  6.3. Probability  6.3.1. Simple Events  6.3.2. Experimental Probability  6.3.3. Theoretical Probability
  7. Practical Geometry  7.1. Construction of Triangles  7.1.1. Constructing Triangles Given Side Lengths  7.1.2. Constructing Triangles Given Side and Angle  7.1.3. Constructing Right-Angled Triangles  7.2. Construction of Quadrilaterals  7.2.1. Quadrilaterals Given Side Lengths and Angles  7.2.2. Constructing Parallelograms and Rectangles

Grade 7 → Geometry ↓


Lines and Angles


In geometry, lines and angles are the fundamental building blocks. It is essential to understand these basic concepts to delve deeper into the study of mathematics and shapes. In this detailed explanation, we will learn about lines and angles, their types, properties, and their contribution to the formation of various geometric shapes.

Lines

A line is a straight one-dimensional figure that has no thickness and extends to infinity in both directions. Here are some important facts about lines:

  • Line: It is defined by two points and extends endlessly in both directions. It is usually represented by a double-headed arrow at two points. Example: AB is a line if it passes through points A and B. 
    Line: ↔AB

Types of lines

There are several types of lines in geometry:

  • Parallel Lines: These are two lines in the same plane that will never meet, no matter how far they are extended. Parallel lines have the same slope.
  • Perpendicular Lines: These are two lines that cut each other at right angles (90 degrees).
  • Intersecting lines: When two lines cross each other at a common point, they are called intersecting lines.

Angles

An angle is formed when two lines or rays meet at a common point called the vertex. The space between these two lines or rays is called the angle.

Types of angles

There are several types of angles depending on the measure:

  • Acute Angle: An angle that is less than 90 degrees.
  • Right Angle: An angle that is exactly 90 degrees.
  • Obtuse Angle: An angle that is more than 90 degrees but less than 180 degrees.
  • Straight Angle: An angle that is exactly 180 degrees.
  • Reflex Angle: An angle that is more than 180 degrees but less than 360 degrees.

Adjacent angles

Adjacent angles are two angles that have a common side and a common vertex. They are right next to each other. Here's an example:

Angle 1 Angle 2

In the above figure, angle 1 and angle 2 are adjacent angles that share the same vertex and side.

Complementary and supplementary angles

  • Complementary angles: Two angles whose sum is 90 degrees. Example: 
    If Angle A = 30° and Angle B = 60°, then A + B = 90°.
  • Supplementary angles: Two angles whose sum is 180 degrees. Example: 
    If Angle C = 120° and Angle D = 60°, then C + D = 180°.

Vertical angles

Vertical angles are the angles that are opposite to each other when two lines intersect each other. They are always equal. Here is a visual representation:

Angle A Angle B

Here, angle A and angle B are vertical angles and are equal.

Properties of parallel lines and a transversal

When a transversal intersects two parallel lines, several pairs of angles are formed. Let us learn about them:

  • Corresponding angles: When two lines are cut by another line (oblique line), then the angles formed in the corresponding corners are called corresponding angles. These angles are equal to each other. 1 2
  • Alternate interior angles: These are on opposite sides of the transversal but inside the two lines. They are equal when the lines are parallel. 3 4
  • Alternate exterior angles: These are on opposite sides of the transversal but outside the two lines. They are also equal when the lines are parallel. 5 6
  • Consecutive interior angles: These are on the same side of the transversal and inside the two lines. Their sum is equal to 180 degrees. 
    Angle 7 + Angle 8 = 180°

Conclusion

Understanding lines and angles and their properties is an important step in geometry. It helps in solving complex problems and forms the basis for learning about various geometric shapes and figures. By familiarizing yourself with these basic concepts, as well as practicing many examples, you can gain a strong grip on this important mathematical topic.


Grade 7 → 4.1


U
username
0%
completed in Grade 7

← Prev (4)
Geometry
Next (4.1.1) →
Types of Angles

Comments 



Lines and Angles

https://www.buddymath.com/g7/4.1?bmal=en