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©1998 ThinkQuest
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©1998 ThinkQuest
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| Theorem 4.1 | In a right triangle, the two angles other than the right angle are complementary and acute. |
| Postulate 15 | SAS Postulate for Congruence of Triangles: If two sides and the included angle of one triangle are congruent to the corresponding two sides and included angle of a second triangle, then the triangles are congruent. |
| Postulate 16 | SSS Postulate for Congruence of Triangles: If the three sides of one triangle are congruent to the corresponding three sides of a second triangle, then the triangles are congruent. |
| Postulate 17 | ASA Postulate for Congruence of Triangles: If two angles and the included side of one triangle are congruent to the corresponding two angles and included side of a second triangle, then the triangles are congruent. |
| Theorem 4.2 | Third Angle Theorem: If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent. |
| Theorem 4.3 | AAS Theorem: If two angles and a nonincluded side of one triangle are congruent to the corresponding two angles and side of a second triangle, then the triangles are congruent. |
| Theorem 5.1 | If two sides of a triangle are congruent, then angles opposite these sides are congruent. (The base angles of an isosceles triangle are congruent.) |
| Corollary | If a triangle is equilateral, then it is also equiangular, and the measure of each angle is 60. |
| Theorem 5.2 | If two angles of a triangle are congruent, then the sides opposite these angles are congruent. |
| Corollary | If a triangle is equiangular, then it is also equilateral. |
| Theorem 5.3 | Hypotenuse-Leg (HL) Theorem: Two right triangles are congruent if the hypotenuse and a leg of one are congruent, respectively, to the hypotenuse and corresponding leg of the other. |
| Theorem 5.4 | The altitude from the vertex angle to the base of an isosceles triangle is a median. (The altitude bisects the base.) |
| Theorem 5.5 | Corresponding medians of congruent triangles are congruent. |
| Theorem 5.6 | Corresponding altitudes of congruent triangles arc congruent. |
| Theorem 5.7 | The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base. |
| Corollary | The bisector of the vertex angle of an isosceles triangle Is also a median and an altitude of the triangle. |
| Theorem 5.8 | A line containing two points, each equidistant from the endpoints of a given segment, is the perpendicular bisector of the segment. |
Note: The concepts in this collection may
not be entirely accurate.
They are for reference only.
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