Congruent Triangles Graphic Organizer
Accelerated Geometry Name______________________________
Geometry Prerequisite Notes Date_______________________________
Congruent Triangles Vs. Similar Triangles Graphic Organizer
|Congruent Triangles ([pic]) |Similar Triangles ([pic]) |
|Having the same size and shape. All corresponding parts are equal. |Having the same shape, but not necessarily the same size. All corresponding angles |
| |are equal and corresponding sides are proportional. |
|Geometric Transformations |
|Isometries |Dilation- |
|Translation, Reflection, Rotation |Transformation that changes the size of a figure, but not the shape. |
| |(x, y) (kx, ky) |
| |k is called the scale factor. |
|Proving Triangles Congruent and Similar |
|Term/ |Definition/Explanation |Term/ |Definition/ |Diagram |
|Postulate | |Postulate |Explanation | |
| |If 3 sides of 1 triangle are congruent to 3|Side – Side - Side |If the three sides of one | |
| |sides of another triangle, then the 2 |SSS |triangle are proportional to | |
|Side – Side - Side |triangles are congruent. | |the three corresponding sides|[pic] |
|SSS | | |of another triangle, then the| |
| | | |triangles are similar |ρABC ∼ ρDEF |
| |If 2 sides and the included angle of one |Side-Angle-Side |If two sides of one triangle |[pic] |
| |triangle are congruent to 2 sides and the |SAS |are proportional to two sides| |
| |included angle of another triangle, then | |of another triangle and their| |
|Side-Angle-Side |the 2 triangles are congruent. | |included angles are |ρABC ∼ ρDEF |
|SAS | | |congruent, then the triangles| |
| | | |are similar. | |
| |If 2 angles and the included side of one |Angle- Angle |If two angles of one triangle|[pic] |
| |triangle are congruent to 2 angles and the |AA |are congruent to two angles |ρABC ∼ ρDEF |
|Angle – Side - Angle |included side of another triangle, then the| |of another triangle, then the| |
| |2 triangles are congruent. | |triangles are similar. | |
|ASA | | | | |
| |If 2 angles and one non-included side of | |
| |one triangle are congruent to 2 angles and | |
| |one non-included side of another triangle, | |
|Angle-Angle-Side |then the 2 triangles are congruent. | |
|AAS | | |
Vocabulary
|Word |Definition/Rule |Illustration/Example |
|Complmentary Angles | | |
|Linear Pair | | |
|Vertical Angles | | |
|Adjacent Angles | | |
|Alternate Interior Angles | | |
|Corresponding Angles | | |
|Alternate Exterior Angles | | |
|Triangle Angle Sum Theorem | | |
|Exterior Angle Theorem | | |
|Scalene Triangle | | |
|Isosceles Triangle | | |
|Angle Bisectors | | |
|Incenter | | |
|Medians | | |
|Centroid | | |
|Midsegment Theorem | | |
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