A line is straight and continues forever in both directions. Lines can't be congruent, because it's impossible to measure their lengths. However, you can measure a line segment, which is the part of a line between two points. Each point is identified with a letter. Line segments with the same length are congruent. Indicate this with the congruent symbol, "≅"; for example, line segment AB ≅ line segment CD.
A ray is part of a line with a definite starting point but no end point. An angle is formed by two rays with a common starting point. Angles are congruent if they have the same measurement in degrees. You can write this with the angle names and congruent sign. Name each angle with three letters -- one point on each ray and the starting point in the middle; for example: <ABC ≅ <DEF. We know some angles are congruent without measuring them. For example, all right angles are congruent. Also, vertical angles form when two lines intersect in an "X" shape. With vertical angles, the angles opposite each other are congruent.
Triangles are congruent if the measurements of their angles and sides are the same. To identify a triangle, give each corner a letter. To show that triangles are congruent, identify them and use the congruent symbol; for example, ∆JKL ≅ ∆MNO. You don't have to measure all parts of triangles to know they're congruent. If the sides of one triangle are exactly the same length as the sides of another, they're congruent. You know that triangles are congruent if two sides and the angle in between them -- the included angle -- are identical. Also, triangles are congruent if they have two angles and one side that are the same. For both triangles, the sides must be in the same location in relation to the angle.
Polygons are closed shapes with straight lines, such as triangles, squares and pentagons. Like triangles, other polygons are congruent when they are exactly the same size and shape. That means two polygons must have the same number of sides. The matching sides must the the same length and the matching angles must have the same measurement.
Circles are congruent when they are exactly the same size. You know two circles are identical by measuring the radius, diameter or circumference of each. The radius is the distance from the circle's center to its edge. The diameter stretches from one side through the center to the other side. The circumference is the distance around the circle. If any one of these is the same for two circles, they're congruent.