Congruent Triangles
What is "Congruent" ... ?
It means that one shape can become another using Turns, Flips and/or Slides:
(see Congruent for more info)
Congruent Triangles
If two triangles are congruent they will have exactly the same three sides and exactly the same three angles.
The equal sides and angles may not be in the same position (if there is a turn or a flip), but they will be there.
Same Sides
If the sides are the same then the triangles are congruent.
For example:
because they all have exactly the same sides.
But:
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is not congruent to: |
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because the two triangles do not have exactly the same sides.
Same Angles
Does this also work with angles? Not always!
Two triangles can have the same angles but be different sizes:
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is not congruent to: |
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because, even though all angles match, one is larger than the other.
But they could be congruent if they are the same size:
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is congruent to: |
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because they are (in this case) the same size
So just having the same angles is no guarantee they are congruent.
Other Combinations
There are many other combinations (for example,"ASA": two angles and the included side). Read more at How To Find if Triangles are Congruent
Marking
If two triangles are congruent, we often mark corresponding sides and angles like this:
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is congruent to: |
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The sides marked with one line are equal in length. Similarly for the sides marked with two lines and three lines.
The angles marked with one arc are equal in size. Similarly for the angles marked with two arcs and three arcs.
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