Congruent Triangles
Table Of Contents
🎬 Math Angel Video: Triangle Congruence Rules
What are Congruent Triangles?
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🛎️ Definition of Congruent Triangles
Two triangles are congruent if they have exactly the same size and shape.
This means:
- They have the same side lengths
- They have the same angle sizes
🛎️ Example of Congruent Triangles
Look at the two triangles.
- Both have side lengths of 3 cm, 5 cm, and 6 cm
- Both have angles of 50°, 60°, and 70°
It does not matter if these triangles are rotated, flipped, or moved. Since their sides and angles are all the same, they are congruent triangles.
How to Tell If Two Shapes Are Congruent?
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If you can move, flip, or turn one shape so it matches another perfectly, the two shapes are congruent.
🛎️ Ways to Move a Shape Without Changing Its Size or Shape:
Translating: moving the shape to a new position.
Reflecting: flipping the shape over a line (mirror line).
Rotating: turning the shape around a fixed point.
Other movements: any combination of the above transformations.
How to Identify Congruent Triangles (4 Rules)?
To prove that two triangles are congruent, you only need to match certain parts. There are 4 rules for triangle congruence:
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1. SSS (Side, Side, Side)
Two triangles are congruent if their 3 corresponding sides are of equal length.
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2. SAS (Side, Angle, Side)
Two triangles are congruent if two sides and the angle between them are the same.
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3. ASA (Angle, Side, Angle)
Two triangles are congruent if two angles and the side between them are the same.
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4. RHS (Right angle, Hypotenuse, Side)
Two right-angle triangles are congruent if they have the same hypotenuse and one identical side.
A Common Mistake in Checking Triangle Congruence
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AAS (Angle-Angle-Side) and SSA (Side-Side-Angle) are not congruence rules. They do not guarantee congruent triangles, because these conditions can create two different triangle shapes.
🚨 Key Point: How to Use ASA and SAS Correctly
When using ASA, the matching side must be between the two matching angles (the included side), not just any side.
When using SAS, the matching angle must be between the two matching sides (the included angle), not just any angle.
🍪 Quiz: Test Your Skills on Congruent Triangles
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