Definition: Triangles space congruent once all matching sides and interior angles space congruent.The triangles will have actually the exact same shape and size, but one may be a mirror image of the other.
You are watching: These are angles, segment, triangles etc. that have exactly the same measures.
In the basic case below, the two triangles PQR and also LMN are congruentbecause every matching side has the same length, and also every equivalent angle has actually the same measure.The edge at P has actually the same measure (in degrees) together the edge at L, the next PQ is the same size as the side LM etc.
In the chart above, the triangles are drawn next to every other and it is evident they are identical.However, one triangle may be rotated, flipped end (reflected), or the two triangles might share a usual side.These cases are discussed further on various other pages:
Imagine the triangles are cardboard
One means to think around triangle congruence is to imagine they space made of cardboard. They are congruent if you have the right to slide them around, revolve them, and also flip them end in various ways so they make a pile where they precisely fit end each other.
How come tell if triangles space congruentAny triangle is identified by six procedures (three sides, 3 angles). But you don"t must know all of them to show that 2 triangles room congruent. Various teams of 3 will do. Triangles room congruent if:
AAA does not work.
If every the corresponding angles the a triangle space the same, the triangles will certainly be the same shape, yet not have to the same size.For more on this seeWhy AAA doesn"t work.
They room called comparable triangles (See similar Triangles).
SSA does not work.
Given 2 sides and a non-included angle, the is feasible to attract two different triangles that fulfill the the values.It is therefore not enough to prove congruence.See Why SSA doesn"t work.
ConstructionsAnother means to think about the above is to ask if it is feasible to build a distinctive triangle given what friend know. Because that example, If you were offered the lengths of two sides and the contained angle (SAS), over there is only one feasible triangle you could draw.If you drew two the them, they would be the same shape and size - the definition of congruent.For more on constructions, see development to Constructions
Properties of Congruent Triangles
If 2 triangles space congruent, then each component of the triangle (side or angle) is congruent come the corresponding part in the various other triangle.This is the true worth of the concept; when you have proved two triangles room congruent, you can find the angle or political parties of among them indigenous the other.
To psychic this necessary idea, some find it useful to use the acronym CPCTC,which means "Corresponding Parts that Congruent Triangles are Congruent".
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In enhancement to sides and also angles, all other properties of the triangle space the exact same also, such as area, perimeter, location of centers, circles etc.