Important CAT Geometry Formulas 2025, Check Definitions & Theorems

Important CAT Geometry Formulas 2025: Geometry is an important part of the Quantitative Aptitude section in the CAT 2025 exam. Many students find this topic difficult. To solve geometry questions quickly and correctly, candidates must know the basic formulas and theorems. But it’s not just about learning them by heart, test takers also need to understand how and when to use them. The CAT 2025 Exam is expected to be held on 30th November 2025. Continue reading this blog to know more about the important CAT Geometry Formulas for 2025, explain why they matter, and share some useful tips to prepare well.

Why are CAT Geometry Formulas Important for CAT 2025?

To do well in the CAT Quant Section, aspirants must know the geometry formulas well. These formulas will help to solve problems faster and save time. Geometry questions are not just limited to one section. Many times, candidates need to use geometry in Data Interpretation and Mensuration problems too. So, understanding these formulas is very important for improving overall score in the CAT 2025 Exam.

Basic CAT Geometry Formulas and Concepts 2025

In this section, candidates can learn the important geometry topics for CAT 2025. Check out the following section for CAT Geometry formulas, definitions, and key theorems. 

Angles and Their Properties

Understanding various types of angles and their relationships is the main part of geometry. These definitions are important for interpreting diagrams and setting up equations.

• Acute Angle: An angle less than 90∘.
• Right Angle: An angle exactly equal to 90∘.
• Obtuse Angle: An angle greater than 90∘ but less than 180∘.
• Straight Angle: An angle exactly equal to 180∘.
• Reflex Angle: An angle greater than 180∘ but less than 360∘.
• Complementary Angles: Two angles whose sum is 90∘.
• Supplementary Angles: Two angles whose sum is 180∘.
• Adjacent Angles: Angles sharing a common side and vertex.
• Linear Pair: Two adjacent angles that form a straight line, summing to 180∘.
• Angle Bisector: A line segment that divides an angle into two equal parts.

CAT Geometry Formulas 2025: Important Properties and Theorems of Triangles

Triangles are foundational shapes in geometry, and a deep understanding of their properties and associated theorems is important for the CAT 2025 exam. These principles govern the relationships between sides and angles. 

Key Properties of a Triangle:

The key properties of a Triangle are as given below- 

• Sum of Angles: The sum of all angles in a triangle is always 180∘.
• Triangle Inequality Theorem: The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
• Difference of Sides: The difference between any two sides of a triangle must be less than the length of the third side.
• Area of Triangle: Area = 1/2×base×perpendicular height.

Important Theorems of Triangles:

The important theorems of Triangles are as given below- 

• Basic Proportionality Theorem (BPT) / Thales Theorem: If a line parallel to one side of a triangle intersects the other two sides, it divides the two sides proportionally.
• Midpoint Theorem: The line segment connecting the midpoints of two sides of a triangle is parallel to the third side and half its length.
• Apollonius’ Theorem: In a triangle △ABC with median AD to side BC, AB2+AC2=2(AD2+BD2).
• Interior Angle Bisector Theorem: An angle bisector of a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle.
• Exterior Angle Bisector Theorem: The bisector of an exterior angle of a triangle divides the opposite side externally in the ratio of the sides containing the angle.

Check Important Quant Formulas for CAT Preparation 2025, Check Key Formulas

CAT Geometry Formulas 2025 for Polygons

Polygons are closed figures formed by straight line segments. Understanding their properties and formulas is important for solving problems related to multi-sided figures.

Key Properties and Formulas for Polygons:

The key properties and formulas for Polygon are as given below- 

• Interior and Exterior Angles: Interior Angle + Exterior Angle = 180∘.
• Number of Diagonals: For an n-sided polygon, Number of diagonals = n(n−3)/2.
• Sum of Exterior Angles: The sum of all exterior angles of any polygon = 360∘.
• Each Exterior Angle (Regular Polygon): Each exterior angle = 360∘/n.
• Sum of Interior Angles: Sum of all interior angles = (n−2)×180∘.
• Each Interior Angle (Regular Polygon): Each interior angle = (n−2)×180∘/n.
• Area of a Regular Polygon: Area = 1/2×Perimeter×Apothem.

CAT Geometry Formulas 2025 for Quadrilaterals

Quadrilaterals are four-sided polygons, each with unique properties and area formulas. Mastering these distinctions is vital for diverse problem types.

Types of Quadrilaterals and Their Properties:

The types of Quadrilaterals and their properties are as given below- 

• Parallelogram: Opposite sides are equal and parallel. Diagonals bisect each other.
• Rectangle: Opposite sides are equal, all angles are 90∘. Diagonals are equal and bisect each other.
• Square: All sides are equal, all angles are 90∘. Diagonals are equal, bisect each other at 90∘.
• Rhombus: All sides are equal. Diagonals bisect each other at 90∘.
• Trapezium (Trapezoid): Only one pair of opposite sides is parallel.
• Kite: Two pairs of adjacent sides are equal. Diagonals are perpendicular.

Area Formulas for Quadrilaterals:

The area-related formulas for Quadrilaterals are as given below- 

• Square: side2
• Rectangle: length×breadth
• Parallelogram: base×height
• Trapezium: 1/2×(sum of parallel sides)×height
• Rhombus: 1/2×d1​×d2​ (where d1​ and d2​ are diagonals)

CAT Geometry Formulas 2025 for Circles

Circles are fundamental geometric shapes with specific formulas related to their area, circumference, and parts. The key formulas for Circles are as given below- 

• Area of Circle: πr2
• Circumference: 2πr
• Arc Length: (θ/360)×2πr (where θ is the central angle in degrees)
• Sector Area: (θ/360)×πr2 (where θ is the central angle in degrees)

CAT Coordinate Geometry Formulas 2025

Coordinate geometry bridges algebra and geometry, allowing geometric shapes to be described using numerical coordinates. The important coordinate geometry formula for CAT 2025 are as given below- 

• Distance Formula: Square root of [(x2​−x1​)2+(y2​−y1​)2]​
• Midpoint Formula: ((x1​+x2​)/2,(y1​+y2​)/2)
• Slope Formula: (y2​−y1​)/(x2​−x1​)
• Section Formula (Internal Division): ((mx2​+nx1​)/(m+n),(my2​+ny1​)/(m+n))
  • (Divides a line segment in the ratio m:n)

Check CAT Quantitative Syllabus 2025, Topics, Best Books, Preparation Tips

Final Thoughts

Geometry may look difficult at first because of its many shapes, lines, and formulas. But to do well in the CAT Quant section, aspirants should understand the basic formulas and keep practising. Each of the geometry formula is important to solve any shape, area, circumference, etc.m related questions. Take your time to learn the formulas and theorems regularly. Additionally, candidates should draw diagrams to understand better. With regular practice and growing confidence, geometry can become one of the easiest and highest-scoring topics in the CAT 2025 exam.