![]() ![]() ![]() In other words, two line segments have equal lengths if they are congruent. Two line segments are said to be congruent if their lengths are the same. ![]() Line segments also make up the sides of the plane figures. ![]() In geometry, a line segment is a fundamental figure that is created by joining any two points on a plane figure. Congruent line segments can, but are not required to, be parallel, perpendicular, or at any other particular angle. Its beginning and end points are known, so its length can be calculated. An exact starting point and ending point define a straight line segment. Congruent Line SegmentsĪ pair of equal-length line segments makes up the congruent segment. The separation between two points determines the length of a line segment. They are flexible and can be in any position or orientation. If two line segments are of the same length, they are said to be congruent. The two figures are equal to one another and are referred to as congruent figures when you transform one figure into another by a series of rotations and/or reflections. Congruent FiguresĬongruent figures are geometric objects that share the same size and shape in mathematics. Congruence of plane figures is the name of the relationship in use. If two plane figures, such as line segments, angles, and other figures, are similar in size and shape, they are said to be congruent. The sides of the plane figures are the straight lines or curves that make them up. Some of the plane figures include line segments, curves, or a combination of both line segments and curves. Congruence of Plane figuresĪ geometric figure with no thickness is called a plane figure. The following figures show some of the basic plane shapes: triangles, squares, rectangles, and circles. A vertex is the point where two sides meet, and a side is a straight line that is part of the shape. Different plane shapes have various characteristics, such as various vertices. Plane FiguresĪ plane shape is a closed, 2-D, or flat figure. Congruence is the name given to the relationship between two congruent figures. However, this article will only discuss the congruence of plane figures.įigures that are consistent in size and shape are said to be congruent. The 2-D and 3-D figures are both consistent with each other. Congruent figures in mathematics are those that share the same size and shape. If two shapes are equivalent to one another in all conceivable ways, they are said to be congruent. If two squares have sides of the same length, they are said to be congruent.If the corresponding sides of two rectangles are equal, they are said to be congruent.If the sides and angles of two triangles are the same, they are said to be congruent.Two circles should have the same diameter if they are congruent.RHS rule states that if in a right angled triangle hypotenuse and one side are equal, the two triangles are congruent.Only when two figures have the same size and shape, including their sides, points, angles, etc., can they be said to be congruent.ASA congruence rule states that if two angles and a side in the middle of the two angle are equal, the triangles are congruent.SAS congruence rule states that if two sides and an angle in the middle of the two sides are equal, the two triangles are congruent.SSS congruence rule states that if all sides of a triangle are equal, the triangles are congruent.There are 4 rules to determine if two triangles are congruent: SSS, SAS, ASA, RHS.Congruent triangles are those triangles whose sides and angles are exactly equal.If all the three corresponding sides of two triangles are equal then they are said to be congruent by SSS rule. RHS (Right angle- Hypotenuse-Side)- If the hypotenuse and side of one right-angled triangle are equal to the hypotenuse and the corresponding side of another right-angled triangle, the two triangles are congruent.AAS(Angle-Angle-Side)- Two triangles are said to be congruent by AAS condition if their two angles and 1 side are equal.ASA(Angle-Side-Angle)- Two triangles are said to be congruent by ASA condition if their two angles and 1 side are equal.SAS(Side-Angle-Side)- Two triangles are said to be congruent by SAS condition if their two sides and 1 angle are equal.SSS (Side-Side-Side) – Two triangles are said to be congruent by SSS condition if all three sides are equal.If there are two triangles A and B then if they fulfil any of the below mentioned conditions then they are said to be congruent and they are mentioned like below: So, we can say both triangles ABC and PQR are congruent. ![]()
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