Let’s go step by step to understand what this chart is showing.
This chart lists the
five main ways you can prove that two triangles are congruent — meaning they are exactly the same shape and size, even if they’re flipped or turned.
Here’s what each one means:
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1. SSS (Side-Side-Side)
If all three sides of one triangle match up with all three sides of another triangle (same lengths), then the triangles are congruent.
→ Think: “All sides match → triangles match.”
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2. SAS (Side-Angle-Side)
If two sides AND the angle *between* them in one triangle match two sides and the included angle in another triangle, then they’re congruent.
→ Important: The angle must be *between* the two sides.
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3. ASA (Angle-Side-Angle)
If two angles AND the side *between* them in one triangle match those in another triangle, then they’re congruent.
→ Again, the side has to be *between* the two angles.
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4. AAS (Angle-Angle-Side)
If two angles and a side *not between* them (a side opposite one of the angles) match in both triangles, then they’re congruent.
→ This works because if two angles are known, the third is automatically fixed (since angles in a triangle always add to 180°).
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5. HL (Hypotenuse-Leg)
This only works for
right triangles. If the hypotenuse (longest side) and one leg (shorter side) of one right triangle match those of another right triangle, then they’re congruent.
→ Don’t use this unless you know it’s a right triangle!
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These rules help you avoid measuring everything — you just need to check specific parts to know if two triangles are identical.
Final Answer:
The five ways to prove triangles are congruent are: SSS, SAS, ASA, AAS, and HL. Each requires matching specific combinations of sides and angles as described above.
Parent Tip: Review the logic above to help your child master the concept of ways to prove triangles congruent worksheet.
