Triangle Congruence Game

Triangle Congruence Game
If two triangles are congruent, it means that they are exactly the same size and shape. While there are six parts to check (three sides and three angles), geometry provides shortcuts called Congruence Postulates and Theorems that allow you to prove congruence by only checking three specific parts. The shortcuts are SSS, SAS, ASA, AAS. Scroll down the page for a more detailed explanation.
 
In this game, two triangles are generated with sides are marked with tick marks and angles are marked with arcs inside the vertices. Identify the congruence rule or determine if they are not congruent. If you give a wrong answer, the game will provide the correct answer.
 

 

How to Play the Triangle Congruence Game
In this game, you need to practice identifying congruent triangles based on the standard postulates (SSS, SAS, ASA, AAS).
Here’s how to play:

1. Are these Congruent? Look at the two triangles and select SSS, SAS, ASA, AAS or Not Congruent.
   
2. Check Your Work: The game will tell you if you’re correct. If you are wrong, you will be shown the correct answer.
   
3. Get a New Problem: It will then show you a new problem.
   Your score is tracked at the top, showing how many you’ve gotten right out of the total you’ve tried.
   
4. Back to Menu Click “Menu” to restart the game.
    
   

The Four Congruence Shortcuts (Postulates & Theorems)
You only need to verify three specific pairs of corresponding parts to prove congruence:
1. SSS (Side-Side-Side) Postulate
If the three sides of one triangle are congruent to the three corresponding sides of another triangle, then the two triangles are congruent.
Condition:
\( \text{Side}_1 \cong \text{Side}_1\), \(\text{Side}_2 \cong \text{Side}_2\), and \(\text{Side}_3 \cong \text{Side}_3\).
Proof: \(\triangle ABC \cong \triangle DEF\) by SSS.
 
2. SAS (Side-Angle-Side) Postulate
If two sides and the included angle (the angle between the two sides) of one triangle are congruent to the corresponding two sides and the included angle of another triangle, then the two triangles are congruent.
Condition:
\( \text{Side}_1 \cong \text{Side}_1\), \( \text{Angle}_{\text{included}} \cong \text{Angle}_{\text{included}}\), and \( \text{Side}_2 \cong \text{Side}_2\).
Proof: \( \triangle ABC \cong \triangle DEF\) by SAS.
 
3. ASA (Angle-Side-Angle) Postulate
If two angles and the included side (the side between the two angles) of one triangle are congruent to the corresponding two angles and the included side of another triangle, then the two triangles are congruent.
Condition:
\(\text{Angle}_1 \cong \text{Angle}_1\), \(\text{Side}_{\text{included}} \cong \text{Side}_{\text{included}}\), and \(\text{Angle}_2 \cong \text{Angle}_2\).
Proof: \(\triangle ABC \cong \triangle DEF\) by ASA.
 
4. AAS (Angle-Angle-Side) Theorem
If two angles and a non-included side (a side that is not between the two angles) of one triangle are congruent to the corresponding two angles and non-included side of another triangle, then the two triangles are congruent.
Condition: \(\text{Angle}_1 \cong \text{Angle}_1\), \(\text{Angle}_2 \cong \text{Angle}_2\), and \(\text{Side}_{\text{non-included}} \cong \text{Side}_{\text{non-included}}\).
Proof: \(\triangle ABC \cong \triangle DEF\) by AAS.
 
The Special Case for Right Triangles
Right triangles often use a simpler theorem because we already know one angle is 90°.
HL (Hypotenuse-Leg) Theorem
If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent.
Condition: \(\text{Hypotenuse} \cong \text{Hypotenuse}\), and \(\text{Leg} \cong \text{Leg}\).
Proof: \(\triangle ABC \cong \triangle DEF\) by HL.
 
The Combinations That DO NOT Work
It is important to know which combinations of three parts are not sufficient to prove congruence.Combination
Why It Fails
AAA (Angle-Angle-Angle)
Proves similarity, but not congruence.
Triangles can have the same shape (same angles) but be different sizes.
SSA (Side-Side-Angle)
This is often called the “Ambiguous Case.”
This combination can result in zero, one, or two non-congruent triangles. You can often “swing” the non-included side to create two different triangles.
 

The video gives a clear, step-by-step approach to learn about triangle congruence.

• Show Video

 

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