Congruent Segments

In geometry, congruent means identical in shape and size. Congruence can be applied to line segments, angles, and figures. Any two line segments are said to be congruent if they are equal in length.

Indicating congruence in line segments

We denote congruence in line segments as follows. If segment AB is congruent to segment CD, we write: $\overline{AB}\cong \overline{CD}$

When drawing geometrical figures, two line segments are demonstrated to be congruent by marking them with the same number of small perpendicular marks, as shown below:

In this case, you can tell that $\overline{AB}\cong \overline{CD}$ because they have two of the perpendicular marks, and that $\overline{EF}\cong \overline{HG}$ because they each have one of the perpendicular marks. In this illustration, it would be obvious which sets of line segments are congruent because they are so different in length. However, there could be a case where you are given line segments that are much closer in length or not drawn to scale, and the perpendicular marks would help you know which lines are congruent in that situation.

Fun facts about congruent lines

Optical Illusions – Congruent segments can be used to play a role in optical illusions, such as the Muller-Lyer illusion where two congruent lines appear to be of different lengths because they have arrows at the end pointing in different directions.

Map Projections – In cartography, congruent segments are essential in creating map projections that accurately represent the Earth's surface on a flat plane.

Fractals – In the world of fractals, congruent segments can be found in self-similar patterns, where a shape is made up of smaller, congruent copies of itself.

Origami – Origami often relies on creating congruent segments by folding paper along specific lines, which helps to create intricate and symmetrical designs.

Topics related to the Congruent Segments

Segments

Congruent Figures

Segment Addition Postulate

Flashcards covering the Congruent Segments

Advanced Geometry Flashcards

Common Core: High School - Geometry Flashcards

Practice tests covering the Congruent Segments

Common Core: High School - Geometry Diagnostic Tests

Advanced Geometry Diagnostic Tests

Get help learning about congruent segments

Tutoring is an excellent way to learn about the important topic of congruent segments in geometry. As a basic geometric skill, understanding congruence is essential for higher-level geometrical learning. Therefore, your student must have a thorough understanding of congruent segments, as well as congruent angles and figures, before moving on to more advanced geometry. A tutor can work with your student in a 1-on-1 setting with no distractions, at your student's pace, using methods that match your student's learning style. To get connected with a professional geometry tutor, contact one of the friendly Educational Directors at Varsity Tutors today.