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When Does SSA Work to Determine Triangle Congruence?
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The triangle congruence criteria, SSS, SAS, ASA, all require three pieces of information. It is interesting, however, that not all three pieces of information about sides and angles are sufficient to determine a triangle up to congruence. In this problem, we considered SSA. Also insufficient is AAA, which determines a triangle up to similarity. Unlike SSA, AAS is sufficient because two pairs of congruent angles force the third pair of angles to also be congruent.

Subject:
Geometry
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Why Does ASA Work?
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CC BY
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The two triangles in this problem share a side so that only one rigid transformation is required to exhibit the congruence between them. In general more transformations are required and the "Why does SSS work?'' and "Why does SAS work?'' problems show how this works.

Subject:
Geometry
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Why Does SAS Work?
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CC BY
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For these particular triangles, three reflections were necessary to express how to move from ABC to DEF. Sometimes, however, one reflection or two reflections will suffice. Since any rigid motion will take triangle ABC to a congruent triangle DEF, this shows the remarkable fact that any rigid motion of the plane can be expressed as one reflection, a composition of two reflections, or a composition of three reflections.

Subject:
Geometry
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Why Does SSS Work?
Unrestricted Use
CC BY
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This particular sequence of transformations which exhibits a congruency between triangles ABC and DEF used one translation, one rotation, and one reflection. There are many other ways in which to exhibit the congruency and students and teachers are encouraged to explore the different possibilities.

Subject:
Geometry
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Wolfram MathWorld: MathWorld: Dilation
Read the Fine Print
Educational Use
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This MathWorld site gives a visual description of dilation and the different kinds of dilation in a similarity transformation.

Subject:
Mathematics
Material Type:
Reading
Provider:
Wolfram
Date Added:
12/01/2023
Wolfram MathWorld: Right Triangle
Read the Fine Print
Educational Use
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This site from MathWorld.com offers extensive information on right triangles. The site contains information on numerous characteristics of right triangles, including constructing similar inscribed triangles, altitudes, Pythagorean triplets, and much more.

Subject:
Mathematics
Material Type:
Lesson
Provider:
Wolfram
Provider Set:
MathWorld
Date Added:
08/07/2023