Geometry Chapter 4, 5 Congruent Triangles
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20 terms
Terms | Definitions |
|---|---|
 Triangle Inequality Theorem | The sum of the lengths of any two sides of a triangle is greater than the length of the third side |
| congruent polygons | are congruent only if all corresponding parts are congruent |
| corresponding part | the part of one shape has to be congruent to that same corner on the other shape |
| SSS | If three sides of a triangle are congruent to three sides of another triangle, then the triangles are congruent |
| SAS | If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent |
| ASA | If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent |
| AAS | If two angles and a NON-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent |
| HL | If the hypotenuse and a leg of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent. *Only for use of right triangles |
| Perpendicular Bisector Theorem | If a point is on the perpendicular bisector of a segment, then the point is an equal distance from the endpoints of the segment |
| legs of isosceles triangle | are opposite base |
| base of isosceles triangle | opposite two legs |
| base angle of isosceles triangle | congruent angles on the base |
| vertex angle | point at which the two legs meet (opposite base) |
| Isosceles Triangle Theorem | If two sides of a triangle are congruent, then the angles opposite the sides are congruent |
| Converse of Isosceles Triangle Theorem | If two angles of a triangle are congruent, then the sides opposite the angle are congruent |
| median of a triangle | a segment from a vertex to the midpoint of the opposite side |
| altitude of a triangle | perpendicular segment from a vertex to the line that contains the opposite side |
| SSA | Side-side-angle does NOT prove triangle congruence; exception is with a right triangle (see HL) |
| CPCTC | Corresponding parts of congruent triangles are congruent; once two triangles have been proven congruent (by using SSS, SAS, ASA, AAS, or HL), then we can conclude its parts are congruent through CPCTC |
| AAA | Angle-angle-angle does NOT prove triangle congruence (however, triangles will be similar; only need AA to prove similarity) |
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