In the figure shown below triangle ABC is congruent to triangle XYZ by SAS criterion.ĪSA Criterion stands for Angle-Side-Angle Criterion. When two sides and the included angle of a triangle is equal to the the two sides and the included angle of another triangle, then these two traingles are said to be congruent by SAS criterion. SAS is the short form of Side-Angle-Side. Here in the figure given below, triangle ABC is congruent to triangle XYZ by SSS criterion. When the sides of two triangles are the same, they are said to be congruent by SSS criterion. They are SSS criterion, SAS criterion, ASA criterion, AAS criterion, and HL criterion. There are certain criteria to refer two triangles to be congruent. It states that if shape 1 is congruent to shape 2 and shape 2 is also congruent to shape 3, then we can say that shape 1 is congruent to shape 3. Transitive property of congruence involves 3 lines or angles or shapes.Symmetric property of congruence means if shape 1 is congruent to shape 2, then we can say that shape 2 is also congruent to shape 1.Reflexive property of congruence means a line segment, or angle or a shape is congruent to itself at all times.All the three properties are applicable to lines, angles and shapes. They are reflexive property, symmetric property and transitive property. There are three properties of congruence. The curved and straight line markings denote that the corresponding sides and angles are equal. The figure given below, shows two congruent triangles. The transitive property of congruence is only applicable if there are more than 2 angles. The difference between them is that, two triangles are said to be similar, if they have the same shape, but are different in size, whereas two triangles are said to be congruent, if their shapes and size exactly match with each other. Sometimes, the term ''Similar triangles' is confused with 'Conguent triangles'. If one triangle is flipped, rotated or transformed to get the exact shape and size of the second triangle, and it still does not undergo any transformation in its shape, size, angles or any other dimensions, then we can say that the first triangle is congruent to the second triangle. Also, the two triangles have the same side length and angles. Two triangles are said to be congruent if they have the same shape and size. Congruent Triangles and Properties of Congruence
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