How to Use the Triangle Theorems Calculator – Step-by-Step Guide
Geometry Plane Triangle Theorems Calculator
What is Geometry Plane Triangle Theorems Calculator?
The Geometry Plane Triangle Theorems Calculator is an online interactive tool that helps you solve any triangle using classic mathematical theorems and formulas. By entering known side lengths and/or angles, you can instantly find missing sides, angles, area, and other triangle properties.
Plane triangle theorems include rules like the angle sum property, the Pythagoras theorem, the law of sines, law of cosines, and congruence or similarity criteria. This Vedantu calculator is customised for students, teachers, and professionals who want quick solutions to triangle questions using step-by-step maths logic.
Formula or Logic Behind Geometry Plane Triangle Theorems Calculator
The calculator uses key geometry formulas to find unknown values. These include:
- Angle Sum Theorem: A + B + C = 180° (sum of all triangle angles)
- Pythagoras Theorem: a2 + b2 = c2 (for right triangles)
- Law of Sines: a/sinA = b/sinB = c/sinC (ratio for all triangles)
- Law of Cosines: a2 = b2 + c2 - 2bc cosA (for non-right triangles or SAS/SSS)
- Heron's Formula: Area K = √[s(s−a)(s−b)(s−c)] where s is the semi-perimeter (useful when all three sides are known)
- Similarity & Congruence Theorems (like SSS, SAS, ASA, AAS, RHS)
List of Major Triangle Theorems and When to Use Them
| Theorem Name | Formula or Statement | When to Use |
|---|---|---|
| Angle Sum Theorem | Sum of angles A+B+C=180° | To find a missing angle when two are known |
| Pythagoras Theorem | a2 + b2 = c2 | For right-angled triangles |
| Law of Sines | a/sinA = b/sinB = c/sinC | When two angles + one side, or two sides + non-included angle are known |
| Law of Cosines | c2 = a2 + b2 − 2ab cosC | For SSS or SAS (two sides + included angle) triangles |
| Heron's Formula | K = √[s(s−a)(s−b)(s−c)] | To quickly calculate the area when all 3 sides are known |
Steps to Use the Geometry Plane Triangle Theorems Calculator
- Enter all known sides or angles into the input fields (leave unknowns blank)
- Select a specific theorem or leave as 'Auto Select' for the calculator to choose
- Click the 'Calculate' button
- The results and step-by-step solution will appear instantly below
Why Use Vedantu’s Geometry Plane Triangle Theorems Calculator?
This calculator is easy to use, mobile optimized, and provides detailed stepwise working for every result. Students save time on homework and revision and avoid confusion over which theorem fits which question.
It’s trusted by lakhs of students, reviewed by maths educators, and matches the latest NCERT and CBSE geometry topics. Teachers also use it for classroom demo and practice.
Real-life Applications of Geometry Plane Triangle Theorems Calculator
Triangle theorems are used in construction, architecture, navigation, engineering, design, astronomy, and many branches of science.
Whether you’re building a roof, designing a bridge, measuring land plots, or solving maths exams, triangle calculators help turn measurements into accurate results using time-tested formulas.
Sample Triangle Theorem Solutions
| Known Values | Theorem Used | Find | Result |
|---|---|---|---|
| a=5, b=12 | Pythagoras | c | c = 13 |
| A=60°, B=80°, c=7 | Angle Sum, Law of Sines | a, b, C | C=40°, a=5.03, b=8.98 |
| a=6, b=8, C=90° | Law of Cosines | c | c=10 |
| a=9, b=13, c=14 | Heron's Formula | Area | K = 51.99 |
| B=50°, C=70°, a=8 | Law of Sines | b, c, A | A=60°, b=9.14, c=10.33 |
You can explore more geometry concepts with our law of sines calculator and law of cosines calculator. For finding triangle area using only sides, try the Heron's formula calculator, or solve right triangles with the Pythagorean theorem calculator.
For converting triangle-related measurements, see centimeter to meter calculator or square footage calculator for area conversions.
Download our free PDF: “List of Triangle Theorems with Proofs (CBSE/ICSE)” for offline reference and deeper understanding.
