Important CAT Geometry Formulas 2025 PDF Download with Solutions and Answers

Overview: Geometry is a scoring topic of the the QA section of the CAT exam, testing spatial reasoning and logical thinking. To ace this section you need to have good hold on the CAT geometry formulas and theorems. Read the blog to know more about them!

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• Geometry includes triangles, circles, quadrilaterals, polygons, and coordinate geometry. 
• These all shapes have their individual formulas and theorems based on which questions are asked in the CAT exam 2025

In this blog, we will guide you through the essential 20+ CAT Geometry Formulas, break down their importance, and provide expert tips to enhance your preparation.

Additionally, we’ll recommend some of the best books for CAT Geometry that can further solidify your knowledge and ensure you’re well-prepared for the exam.

Read More: Complete CAT Geometry Syllabus

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Importance of CAT Geometry Formulas 2025

The importance of CAT Geometry formulas lies in their critical role within the Quantitative Aptitude section of the exam. Geometry contributes a significant portion to this section, making it essential for candidates to understand and memorize key formulas. A solid grasp of these formulas allows aspirants to solve problems quickly and accurately, eliminating the need to derive them during the exam. This time-saving factor is crucial, as every second counts in CAT. Furthermore, many advanced questions in the exam are based on fundamental geometry concepts, making a strong foundation vital for solving more complex problems.

In addition to direct geometry problems, these formulas are often necessary for solving Data Interpretation sets, where spatial reasoning and geometric relationships are tested. The versatility of geometry formulas across various topics such as mensuration, coordinate geometry, and polygons makes them even more important for overall success.

A clear understanding of these formulas not only improves accuracy but also boosts candidates' confidence. With the ability to solve geometry-related questions swiftly and correctly, aspirants are well-equipped to achieve a higher score and improve their chances of securing a top percentile in the CAT exam.

CAT 2025 Geometry Angles and Properties

The geometry topic consist of types of angles, including complementary, adjacent, obtuse, and right angles.

Angle Type	Definition
Acute Angle	The angle is less than 90∘.
Right Angle	The angle is equal to 90∘.
Obtuse Angle	The angle that is greater than 90∘ but less than 180∘.
Straight Angle	The angle that is equal to 180∘.
Reflex Angle	The angle which is greater than 180∘ but less than 360∘.
Complementary Angles	Two angles, whose sum is 90∘, are complementary to each other.
Supplementary Angles	Two angles, whose sum is 180∘, are supplementary to each other.
Adjacent Angles	Adjacent angles must have a common side.
Linear Pair	One side must be common (e.g., OB), and these two angles must be supplementary (sum to 180∘).
Angle Bisector	A line segment that divides an angle equally into two parts and is equidistant from the two sides.

Important Properties of a Triangle

Property 1: The sum of all the angles of a triangle = 180°

Property 2:The sum of the lengths of the two sides > the length of the third side

Property 3: The difference between any two sides of any triangle < length of the third side

Property 4:The area of any triangle can be found by using this formula:

Area of any triangle = 1/2 × base × perpendicular to base from the opposite vertex.

Check: How to prepare for Quantitative Aptitude for CAT exam

Some Important Theorems of Triangles in CAT Geometry 2025

The list of important theorems of the Triangle includes:

1. Basic Proportionality Theorem (BPT)

Any line parallel to one side of a triangle divides the other two sides proportionally. So, if DE is drawn parallel to BC, then it would divide sides AB and AC proportionally.

2. Midpoint Theorem

Any line joining the mid-points of two adjacent sides of a triangle is joined by a line segment, and then this segment is parallel to the third side.

3. Apollonius’ Theorem

In a triangle, the sum of the squares of any two sides of a triangle is equal to twice the sum of the square of the median to the third side and the square of half the third side.

4. Interior Angle Bisector Theorem

In a triangle, the angle bisector of an angle divides the opposite side to the angle in the ratio of the remaining two sides

5. Exterior Angle Bisector Theorem

In a triangle, the angle bisector of any exterior angle of a triangle divides the side opposite to the external angle in the ratio of the remaining two sides

Check: How to prepare for Logical Reasoning for CAT 

CAT Geometry Formulas 2025 for Polygons and Their Properties

Key Properties and CAT geometry formulas of a Polygon

• Interior and Exterior Angles: Interior Angle + Exterior Angle = 180°

• Diagonals: Number of diagonals in an n-sided polygon = n(n - 3) / 2

• Exterior Angles:

• The sum of all exterior angles of any polygon = 360°
• Measure of each exterior angle of a regular polygon = 360° / n
• Ratios:
• Ratio of sides to diagonals in an n-sided polygon = 2 : (n - 3)
• Ratio of interior angle to exterior angle in a regular polygon = (n - 2): 2

• Interior Angles:
  • Sum of all interior angles of any polygon = (2n - 4) × 90° or (n-2) x 180°
  • Each interior angle of a regular polygon = [(2n - 4) × 90°] / n or [(n-2) x 180°] / n
• Similarity: Two polygons are similar if:
  • Their corresponding angles are equal.
  • Their corresponding sides are proportional.

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CAT Geometry Formulas 2025 for Quadrilaterals and their Properties

1. Parallelogram

• Opposite sides are equal in length and parallel (like train tracks that never meet).
• The lines that cut across from corner to corner (diagonals) cut each other in half.

2. Rectangle

• Opposite sides of the quadrilateral are equal.
• All angles are right angles (90 degrees, like a corner of a square).
• The diagonals are equal in length and cut each other in half.

3. Square

• All sides of the square are equal.
• All angles are right angles (90 degrees).
• The diagonals cut each other in half at a perfect right angle (90 degrees).

4. Rhombus

• All sides are equal.
• The diagonals cut each other in half at a perfect right angle (90 degrees). (Think of a diamond shape.)

5. Trapezium (or Trapezoid)

• Only one pair of opposite sides is parallel.

6. Kite

• Two pairs of sides next to each other are equal in length.
• The diagonals cut each other at a perfect right angle (90 degrees).

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CAT Geometry Formulas 2025 for Circles

Here are the key formulas for Circles:

Concept	Formula
Area of Circle	πr²
Circumference	2πr
Arc Length	(θ/360) × 2πr
Sector Area	(θ/360) × πr

Find: Important Formulas for CAT 2025

CAT Geometry Formulas 2025 for Quadrilaterals

The formula for different quadrilaterals includes the following 

Shape	Area Formula
Square	side²
Rectangle	length × breadth
Parallelogram	base × height
Trapezium	½ × (sum of parallel sides) × height
Rhombus	½ × d₁ × d₂

Check: Venn Diagram Practice Questions for CAT 2025

CAT Geometry Formulas 2025 for Polygons

The different formulas for polygons include:

Concept	Formula
Sum of Interior Angles	(n - 2) × 180°
Each Interior Angle (regular)	(n - 2) × 180° / n
Area of a Regular Polygon	½ × Perimeter × Apothem

CAT Coordinate Geometry Formulas 2025

The important coordinate geometry formulas include:

Concept	Formula
Distance	√[(x₂ - x₁)² + (y₂ - y₁)²]
Midpoint	((x₁ + x₂)/2 , (y₁ + y₂)/2)
Slope	(y₂ - y₁) / (x₂ - x₁)
Section Formula	(mx₂ + nx₁)/(m+n), (my₂ + ny₁)/(m+n)

Click Here: Download CAT Arithmetic questions PDF with Solutions

Essential Geometry Theorems for CAT 2025

Apart from the essential CAT geometry formulas, the candidates also need to learn the important theorems. Some of the key theorems you must know:

Theorem	Explanation
Basic Proportionality Theorem (Thales)	If a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally.
Angle Bisector Theorem	The angle bisector of a triangle divides the opposite side in the ratio of the adjacent sides.
Pythagoras Theorem	Applies only in right-angled triangles.
Similarity of Triangles	If two triangles have corresponding angles equal, they are similar.
Cyclic Quadrilateral	Opposite angles of a cyclic quadrilateral are supplementary.
Tangents from a Point	The tangents drawn from an external point to a circle are equal in length.

Know more: CAT DILR Syllabus Overview

Conclusion

Geometry might seem a bit tricky at first with all the shapes, lines, and formulas. But don't worry! It's all about understanding the basic formulas and theorems and practising regularly. Remember, every shape has a story, and each formula helps you solve a piece of the puzzle. 

So, take your time, learn those key CAT geometry formulas and theorems, and don't be afraid to draw diagrams. 

With a little bit of practice and confidence, you'll find that geometry can actually be one of the most interesting and score-boosting parts of the CAT exam. Grab those geometry notes, keep practising, and get ready to ace those questions!

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