There are many different types of triangles. Congruent triangles are those with three pairs of coordinating sides and three pairs of coordinating angles. Basically, by translating, rotating, and/or flipping one triangle, you can get it to line up exactly with the other triangle. If that is the case, they are congruent.
If one triangle, , and another triangle, , are congruent, we write
In the example below,
But is not congruent with .
Also note, we write that , but not that . The corresponding vertices must come in the correct order.
It's not necessary to measure all three sides and all three angles to determine if two triangles are congruent. There are a handful of ways you can determine congruence by measuring just three sides and/or angles:
Example 1
measures:
measures:
Are and congruent?
Yes, they are, because all three corresponding sides are the same.
Example 2
measures: , and the included
measures: , and the included
Are and congruent?
No, because the included angles A and D are not the same.
Example 3
measures: , and the included Side
measures: , and the included Side
Are and congruent?
No, because the included sides A and D are not the same.
Example 4
measures: , and the non-included Side
measures: , and the non-included Side
Are and congruent?
No, because angles B and E are not the same.
Example 5
is a right-angled triangle that measures: ,
is a right-angled triangle that measures: ,
Are and congruent?
Yes, because both hypotenuses and long legs are the same.
Example 6
measures:
measures:
Are and congruent?
Not enough information is given, because AAA is not a reliable proof for whether a triangle is congruent or not.
A.
measures: , and the included
measures: , and the included
Are and congruent?
No, because angles A and E are not the same.
B.
measures:
measures:
Are and congruent?
Not enough information is given, because AAA is not a reliable proof for whether a triangle is congruent or not.
Common Core: High School - Geometry Flashcards
Common Core: High School - Geometry Diagnostic Tests
Advanced Geometry Diagnostic Tests
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