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If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent. Example: Triangle ABC is congruent to triangle DEF if AB=DE, BC=EF, and angle B is equal to angle E.

If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the straight lines will meet on that side when extended far enough. Example: This postulate is the basis for proving the existence of parallel lines.

All right angles are congruent to each other. For instance, if two angles are both right angles, they are the same size (90 degrees).

If three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent. Example: Triangle ABC is congruent to triangle DEF if AB=DE, BC=EF, and CA=FD.

Given two distinct points, there exists a straight line that connects them. For example, if points A and B are distinct, a line AB can be drawn.

The sum of the angles in a triangle is equal to two right angles (180 degrees). For example, if a triangle has angles of 90, 50, and 40 degrees, their sum is 180 degrees.

If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent. Example: Triangle ABC is congruent to triangle DEF if angle A equals angle D, angle C equals angle F, and side BC equals side EF.

Given any straight line segment, a circle can be drawn having the segment as the radius and one endpoint as the center. For example, with segment AB, a circle with center A and radius AB can be drawn.

If two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, then the triangles are congruent. Example: Triangle ABC is congruent to triangle DEF if angle A equals angle D, angle B equals angle E, and side AC equals side DF.