Two triangles will be equal if any of the following conditions are true: You can determine the congruence of triangles by using their angles together with the congruence of their sides. The four internal angles are congruent and measure 90⁰. In this type of triangle, its three internal angles are congruent and always measure 60⁰. In this type of triangle, two of its internal angles are congruent. In the following figure, you will see that the following pairs are congruent: Those that are opposite each other are vertical angles, these are always congruent.Ī line that intersects two parallels forms congruent angles. When two lines intersect, 4 angles are formed. What type of angles are congruent? Vertical angles
The sine of these angles, on the other hand, is the same. For example, if you take two adjacent angles, one of 120° and the other of 60°, the cosine of the first is equal to that of the second multiplied by -1. Other properties of adjacent angles is that their cosines have the same value, although they have inverse signs. This definition allows you to infer that adjacent angles are also contiguous or consecutive angles (because they have a common side and the same vertex) and supplementary angles (the sum of both results in 180°, which is known as a straight angle). Adjacent is an adjective that describes what is located next to something.Īdjacent angles share a side and the vertex, while the other two sides are opposite rays. What are adjacent angles?Īn angle is a geometric figure that is formed with two rays that share the same vertex as an origin. Two triangles are congruent if they have two sides respectively congruent and the angles opposite the greater of the sides are also congruent. If two angles and the side between them are respectively congruent with the same of another triangle, then the triangles are congruent. Two triangles are congruent if two of their sides and the angle between them are respectively equal. If you have two triangles and the three sides of one are respectively congruent with those of the other, then the triangles are congruent.
These are:įor two triangles to be congruent, it’s enough that only some sides and / or angles are equal. The congruence criteria correspond to the postulates and theorems that state which are the minimum conditions that two or more triangles must meet to be congruent. In many cases, it’s enough to establish the equality between three corresponding parts and use one of the criteria to deduce the congruence of two triangles. The diagonals of a parallelogram also set up congruent vertex angles. That is, if by turning it and/or moving it, they coincide with each other. Two angles are also congruent if they coincide when superimposed. Two angles are said to be congruent if their corresponding sides and angles are of equal measure.