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en.wikipedia.org/wiki/Angle_bisector_theorem

In geometry, the angle bisector theorem is concerned with the relative lengths of the two segments that a triangle's side .... Since supplementary angles have equal sines, .... if a side of a triangle be divided internally or externally so that its segments have the same ratio as the other sides of the triangle, the straight line drawn ...

en.wikipedia.org/wiki/Isosceles_trapezoid

In Euclidean geometry, an isosceles trapezoid is a convex quadrilateral with a line of symmetry ... The diagonals divide each other into segments with lengths that are pairwise equal; in terms of the picture below, AE = DE, BE = CE (and AE ≠ CE ... In an isosceles trapezoid the base angles have the same measure pairwise.

Segments have the same length and angles have the same measure? ... The answer to, "Segments that have the same length" Is Congruent Segments! Edit.

www.mathopenref.com/congruentlines.html

Line segments are congruent if they have the same length. However, they need not be parallel. They can be at any angle or orientation on the plane.

www.mathopenref.com/congruent.html

Two line segments are congruent if they have the same length. ... So if two separate angles have measures of 30° and 23° for example, they are not congruent ...

How do we know if line segments are congruent? Let's watch this example of counting points to see if they have the exact same length. Created by Sal Khan.

www.mathplanet.com/education/geometry/points,-lines,-planes-and-angles/measure-line-segments

The length of a line segment can be measured (unlike a line) because it has two endpoints. ... Two lines could have the same measure but still not be identical.

math.stackexchange.com/questions/915914/what-is-the-difference-between-congruency-and-equality

Sep 1, 2014 ... So, two figures are equal if they have the same points. ... I was taught to say two line segments or two angles are equal if they have the same measure. ... two figures are congruent if their corresponding parts are of the same measurement. Ex. If two segments have equal length, then they are congruent.

slideplayer.com/slide/4491266

5 Congruent Polygons Congruent segments have the same length Congruent angles have the same measure Congruent polygons have the same size and ...