Triangle Congruence Calculator

Test SSS, SAS, ASA, AAS, and RHS rules. Check values, compare measures, and explain conclusions. Build confidence with clean steps, examples, exports, and practice.

Calculator

Triangle 1

Triangle 2

Example Data Table

Method Triangle 1 Triangle 2 Expected Result
SSS AB=5, BC=7, CA=8 DE=5, EF=7, FD=8 Congruent
SAS AB=6, BC=9, Angle B=40 DE=6, EF=9, Angle E=40 Congruent
ASA Angle A=50, Angle B=60, AB=10 Angle D=50, Angle E=60, DE=10 Congruent
AAS Angle B=45, Angle C=80, AB=12 Angle E=45, Angle F=80, DE=12 Congruent
RHS Right angle at A, BC=13, AB=5 Right angle at D, EF=13, DE=5 Congruent

Formula Used

SSS: If three corresponding sides are equal, then the triangles are congruent.

SAS: If two corresponding sides and the included angle are equal, then the triangles are congruent.

ASA: If two corresponding angles and the included side are equal, then the triangles are congruent.

AAS: If two corresponding angles and one non included side are equal, then the triangles are congruent.

RHS: In right triangles, if one hypotenuse and one corresponding leg are equal, then the triangles are congruent.

Perimeter: P = side1 + side2 + side3.

Area: Area = √[s(s-a)(s-b)(s-c)], where s = (a+b+c)/2.

How to Use This Calculator

  1. Select the congruence rule you want to test.
  2. Enter the matching side and angle data for Triangle 1 and Triangle 2.
  3. Use the SAS, ASA, AAS, or RHS helper selectors when needed.
  4. Click the calculate button to see the result above the form.
  5. Review the method, matched parts, side ratios, perimeter, and area details.
  6. Use the CSV button to export the result table.
  7. Use the PDF button to print or save the result as a PDF file.

Triangle Congruence in Everyday Geometry

A triangle congruence calculator helps you test whether two triangles match exactly. It compares sides and angles with standard geometry rules. This saves time during homework, proof writing, exam revision, and classroom practice. A clear result also helps students understand why a rule works.

Congruent triangles have the same size and shape. Their corresponding sides are equal. Their corresponding angles are equal too. Geometry proves congruence with SSS, SAS, ASA, AAS, or RHS. Each rule needs different measurements. This calculator lets you choose the correct method and review the outcome quickly.

Why This Triangle Congruence Calculator Is Useful

Manual checking can be slow. It is easy to mix up matching parts. This tool organizes the values clearly. It compares both triangles, highlights the method used, and reports whether the data supports congruence. It also shows perimeter and area when enough side values are available.

The calculator is helpful for school geometry, tutoring sessions, worksheet practice, and fast verification. It supports right triangle checks through the RHS rule. It also gives export options for records, assignments, and printed study sheets. That makes review easier for teachers and learners.

Understanding the Main Rules

SSS uses three equal corresponding sides. SAS uses two sides and the included angle. ASA uses two angles and the included side. AAS uses two angles and a non included side. RHS works in right triangles with one equal hypotenuse and one equal leg. When one valid rule matches, the triangles are congruent.

Enter values carefully. The chosen rule must match the data you know. ASA needs the side between the two entered angles. AAS needs a side that is not between them. SAS requires the angle between the two given sides. This detail matters in geometry proofs.

Better Proof Writing and Faster Practice

Use the result as a checking step before writing a formal proof. Confirm the correct rule first. Then name the matching vertices carefully. Once congruence is established, corresponding parts can be used later. This improves accuracy and builds confidence in geometry problem solving.

Students can use the example table to see valid inputs. Teachers can use the exports for notes or answer keys. The calculator keeps the process simple, but the reasoning stays mathematical.

FAQs

1. What does triangle congruence mean?

It means two triangles have the same shape and the same size. Their corresponding sides and corresponding angles are equal.

2. Which rules prove triangle congruence?

The standard rules are SSS, SAS, ASA, AAS, and RHS. Each rule needs a specific combination of matching sides or angles.

3. Does AAA prove congruence?

No. AAA only shows similarity, not congruence. The triangles can have equal angles but different side lengths.

4. When should I use SAS?

Use SAS when you know two corresponding sides and the included angle between them for both triangles.

5. Why does ASA need the included side?

ASA depends on the side placed between the two known angles. That side fixes the triangle size and removes ambiguity.

6. What makes RHS different?

RHS only works for right triangles. It uses one right angle, one equal hypotenuse, and one equal corresponding leg.

7. Why are perimeter and area shown?

They add more context when full side data is entered. Congruent triangles also have equal perimeter and equal area.

8. Can I export my result?

Yes. Use the CSV button for spreadsheet data. Use the PDF button to print or save the result section.