Topics
Number Systems
Number Systems
Polynomials
Algebra
Algebraic Expressions
Algebraic Identities
Coordinate Geometry
Linear Equations in Two Variables
Coordinate Geometry
Geometry
Area
Constructions
- Introduction of Constructions
- Geometric Constructions
- Some Constructions of Triangles
Introduction to Euclid’S Geometry
Mensuration
Statistics and Probability
Lines and Angles
- Introduction to Lines and Angles
- Basic Terms and Definitions
- Intersecting Lines and Non-intersecting Lines
- Parallel Lines
- Concept of Pairs of Angles
- Concept of Transversal Lines
- Basic Properties of a Triangle
Probability
Triangles
Quadrilaterals
- Properties of Quadrilateral
- Another Condition for a Quadrilateral to Be a Parallelogram
- Theorem of Midpoints of Two Sides of a Triangle
- Property: The Opposite Sides of a Parallelogram Are of Equal Length.
- Theorem: A Diagonal of a Parallelogram Divides It into Two Congruent Triangles.
- Theorem : If Each Pair of Opposite Sides of a Quadrilateral is Equal, Then It is a Parallelogram.
- Property: The Opposite Angles of a Parallelogram Are of Equal Measure.
- Theorem: If in a Quadrilateral, Each Pair of Opposite Angles is Equal, Then It is a Parallelogram.
- Property: The diagonals of a parallelogram bisect each other. (at the point of their intersection)
- Theorem : If the Diagonals of a Quadrilateral Bisect Each Other, Then It is a Parallelogram
Circles
Areas - Heron’S Formula
- Area of a Triangle by Heron's Formula
- Application of Heron’s Formula in Finding Areas of Quadrilaterals
- Geometric Interpretation of the Area of a Triangle
Surface Areas and Volumes
Statistics
- Definition:Triangle
- Parts of a Triangle
- Basic Properties of a Triangle
- Key Points Summary
Definition:Triangle
A triangle (denoted by the symbol △) is the simplest closed shape in geometry. It is a two-dimensional figure made by connecting three points that do not lie on the same straight line (non-collinear).
Parts of a Triangle
| Triangle |
Name in △ABC |
How to Refer to it |
| Names of Angles | ∠PQR, ∠QRP, and ∠RPQ. |
The angle inside the figure, often simplified to ∠P ∠Q ∠R. |
| Name of Sides | side PQ, side QR, and side RP. |
The three line segments that form the boundary. |
| Names of Vertices | P, Q, and R | The points where two sides meet. |
Basic Properties of a Triangle
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A triangle has 3 sides, 3 vertices, and 3 angles.
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Sum of interior angles of a triangle is always 180°.
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Each interior angle can be denoted using the letter at the vertex.
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A triangle is named using its vertices, and the order does not affect the triangle.
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Each side of the triangle is a line segment joining two vertices.
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Each vertex is a point where two sides meet.
Key Points Summary
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A triangle is formed by 3 non-collinear points joined by line segments.
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It has 3 sides (line segments).
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It has 3 vertices (corner points).
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It has 3 interior angles.
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The sum of interior angles = 180°.
