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Mostly congruent triangles are used for construction of things like bridges and buildings because they are considered more stable and strong to use (i hope that helps i had to learn this for a project) Triangles that have exactly the same size and shape are called congruent triangles. The symbol for congruent is ≅. Two triangles are congruent when the three sides and the three angles of one triangle have the same measurements as three sides and three angles of another triangle. The triangles in Figure 1 are congruent triangles. 





Figure 1 Congruent triangles.


<a href="http://ad.doubleclick.net/jump/CNSite/;navArea=CLIFFSNOTES2_MATH;type=Review_Topic;cat=MATH;kword=geometry;contentItemId=18851;tile=3;sz=300x250;ord=123456789?" target="_blank"><img src="http://ad.doubleclick.net/ad/CNSite/;navArea=CLIFFSNOTES2_MATH;type=Review_Topic;cat=MATH;kword=geometry;contentItemId=18851;tile=3;sz=300x250;ord=123456789?" width="300" height="250" border="0" alt="" /></a> Corresponding parts
The parts of the two triangles that have the same measurements (congruent) are referred to as corresponding parts. This means that Corresponding Parts of Congruent Triangles are Congruent (CPCTC). Congruent triangles are named by listing their vertices in corresponding orders. In Figure 1 , Δ BAT ≅ Δ ICE.
Example 1: If Δ PQR ≅ Δ STU which parts must have equal measurements?




These parts are equal because corresponding parts of congruent triangles are congruent. Tests for congruence
To show that two triangles are congruent, it is not necessary to show that all six pairs of corresponding parts are equal. The following postulates and theorems are the most common methods for proving that triangles are congruent (or equal). Postulate 13 (SSS Postulate): If each side of one triangle is congruent to the corresponding side of another triangle, then the triangles are congruent (Figure 2 ).


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Figure 1 Congruent triangles.


<a href="http://ad.doubleclick.net/jump/CNSite/;navArea=CLIFFSNOTES2_MATH;type=Review_Topic;cat=MATH;kword=geometry;contentItemId=18851;tile=3;sz=300x250;ord=123456789?" target="_blank"><img src="http://ad.doubleclick.net/ad/CNSite/;navArea=CLIFFSNOTES2_MATH;type=Review_Topic;cat=MATH;kword=geometry;contentItemId=18851;tile=3;sz=300x250;ord=123456789?" width="300" height="250" border="0" alt="" /></a> Corresponding parts
The parts of the two triangles that have the same measurements (congruent) are referred to as corresponding parts. This means that Corresponding Parts of Congruent Triangles are Congruent (CPCTC). Congruent triangles are named by listing their vertices in corresponding orders. In Figure 1 , Δ BAT ≅ Δ ICE.
Example 1: If Δ PQR ≅ Δ STU which parts must have equal measurements?




These parts are equal because corresponding parts of congruent triangles are congruent. Tests for congruence
To show that two triangles are congruent, it is not necessary to show that all six pairs of corresponding parts are equal. The following postulates and theorems are the most common methods for proving that triangles are congruent (or equal). Postulate 13 (SSS Postulate): If each side of one triangle is congruent to the corresponding side of another triangle, then the triangles are congruent (Figure 2 ).


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