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# Part 3

 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.