In rectangle ABCD, the angle between AB and AD is 90 degrees and also, in rectangle PQRS angle between PQ and PS is 90 degrees. We observe that in rectangle ABCD BC=AD and in rectangle PQRS QR=SP. We observe that in rectangle ABCD AB=CD and in rectangle PQRS PQ=RS. Here in the above figure, ABCD is one rectangle and PQRS is another rectangle. Two rectangles are said to be congruent if opposite sides are equal and the adjacent sides maintain an angle of 90 degrees.

Therefore we can say that these triangles are congruent. This satisfies the SAS(side, angle, side) criteria for congruency. Here two sides and the corresponding angle of one triangle is equal to two sides and the corresponding angle of another triangle. Two triangles are said to be congruent if they possess two equal sides and a corresponding angle.Īs we observe both the triangles, side BC is equal to side YZ. Case 3: Two equal sides and the corresponding angle of a triangle(SAS: side, angle, side) This satisfies the ASA(angle, side, angle) criteria for congruency. Here two angles and the corresponding side of one triangle is equal to two angles and the corresponding side of another triangle. Angle ABC=Angle XYZ.Īngle A is equal to angle X. Here, in the above figure, ABC is one triangle and DEF is another triangle.Īngle B is equal to angle Y. Two triangles are said to be congruent if they possess two equal angles and a corresponding side. Case 2: Two equal angles and the corresponding side of a triangle(ASA: angle, side, angle) This satisfies the SSS(side,side,side) criteria for congruency. Here, we observe that all three sides of one triangle are equal to the other. Here, in the above figure, ABC is one triangle and XYZ is another triangle.Īs we observe both the triangles, side AB is equal to side XY. Two triangles are said to be congruent if they possess all equal sides. Triangle Case 1: Equal sides for a triangle(SSS: side, side, side) We consider diameter to test congruency of circle and lines to test congruency of triangles etc. Congruency in Different Figuresĭifferent figures follow different criteria to test their congruency. In simple terms, congruency can be defined as two figures trying to prove in either of the ways that they are twins. If two squares are needed to be congruent then they must have all sides equal for both the squares.If two rectangles are needed to be congruent then they must possess equal opposite sides for both the rectangles.If two triangles are needed to be congruent then three sides of one triangle should be equal to three sides of another triangle.Two circles are said to be congruent if the diameter of both circles is the same.ĭifferent figures follow different criteria to be congruent.Two angles are said to be congruent if the angle is the same for both the angles on some common line.Two line segments are said to be congruent if the length of both the lines is the same.In simple terms, we can define this as repositioning or reflecting an object so that it coincides perfectly with some other object without changing its size. This is called a combination of rigid motions or Isometry. Geometrically, when considering a 2 Dimensional object, a set of two points are said to be congruent when one point can be transformed either by translation, rotation, or reflection. Two figures or objects are said to be congruent if one of them is a mirror image of the other or if both of them have the same shape and size. We are providing the detailed concept with the help of examples. Go through the next sections to check the complete details regarding congruent statements and figures. You can know the brief details about how congruency works for each shape.Īre you about congruent topics? If so, Don’t worry! You can get the exact content that you are exploring for. Understand the concept of congruent with the detailed explanation in the next sections. Get the definition of congruency in analytic geometry. Follow the different cases where the lines and angles are said to be congruent.

$geometry congruent shapes$

Check the angles and how they work for each triangle shape. Know the congruent shapes, definitions, and examples here.

Geometry congruent shapes