Congruent Triangles
Learn what congruent triangles are and how to identify them using SSS, SAS, ASA, and RHS. Let's get started! 🚀
Video Lesson
Watch and learn the basics
Flashcards
Review key concepts visually
%20Congruent%20Triangles%20Definition.webp)
%20Congruent%20Triangles%20Rules.webp)
%20Congruent%20Triangles%20(Side-Side-Side).webp)
%20Congruent%20Triangles%20(Side-Angle-Side).webp)
%20Congruent%20Triangles%20(Angle-Side-Angle).webp)
%20Congruent%20Triangles%20(RHS).webp)
%20Congruent%20Triangles%20(Common%20Pitfall).webp)
🛎️ What Are Congruent Triangles?
- Two triangles are congruent if they have the same size and shape.
- This means all corresponding sides and angles are equal.
🛎️ How Can You Recognise Congruent Triangles?
- Congruent triangles can be moved to overlap perfectly.
- This can be done by translating, reflecting, or rotating.
🛎️ SSS (Side-Side-Side)
- Two triangles are congruent if all three corresponding sides are equal.
- The angles do not need to be given.
🛎️ SAS (Side-Angle-Side)
- Two triangles are congruent if two corresponding sides and the included angle are equal.
- The angle must be the included angle.
🛎️ ASA (Angle-Side-Angle)
- Two triangles are congruent if two corresponding angles and the included side are equal.
- The side must be between the two angles.
🛎️ RHS (Right-Angle-Hypotenuse-Side)
- Applies only to right-angled triangles.
- Triangles are congruent if they have the same hypotenuse and one equal side.
🛎️ Common Pitfall
- SSA does NOT guarantee congruence.
- Two equal sides and a non-included angle are not enough to prove congruence.
Practice Questions
Test your understanding
Are these two triangles congruent?
Correct! 🎉 +10 pointsNot quite right
Since all corresponding sides are equal in length, the triangles are congruent by the Side-Side-Side (SSS) congruence rule.
Are these two triangles congruent?
Correct! 🎉 +10 pointsNot quite right
Since the two sides and the included angle are the same in both triangles, they are congruent by the Side-Angle-Side (SAS) rule.
Two right-angled triangles have the same hypotenuse of and one side of . Are these two triangles congruent?
Correct! 🎉 +20 pointsNot quite right
Since the hypotenuse and one side of both right-angled triangles are the same, the Right-Angle Hypotenuse-Side (RHS) rule applies, guaranteeing the triangles are congruent.
Are these two triangles congruent?
Correct! 🎉 +20 pointsNot quite right
The triangles are congruent because they have two equal angles and the side between them is also the same length. This follows the ASA (Angle-Side-Angle) rule.
Which condition cannot be used to determine congruent triangles?
Correct! 🎉 +20 pointsNot quite right
AAS is not enough to prove congruence because it does not always fix the size of the triangle. Different triangles can share the same angles but have different side lengths.
Two triangles each have one side of , another side of . The non-included angle in both triangles is . Are the triangles congruent?
Correct! 🎉 +30 pointsNot quite right
SSA (Side-Side-Angle) does not guarantee congruence. The non-included angle can result in two different triangles, so congruence is not guaranteed.
Want to see the full working?
Interactive Activity
Explore the 4 rules of triangle congruence: SSS, SAS, ASA, RHS
Loading interactive widget...
Click here to open ChatCat