In geometry, a triangle is a figure formed when three JXUwMDM2JXUwMDAxJXUwMDAxJXUwMDBkJXUwMDBjJXUwMDAzJXUwMDAwJXUwMDA1JXUwMDA3JXUw MDBiJXUwMDA0JXUwMDEz points are connected by segments.

Each pair of segments forms an JXUwMDM5JXUwMDBmJXUwMDA5JXUwMDBiJXUwMDA5 of the triangle. The JXUwMDJlJXUwMDEzJXUwMDE3JXUwMDA2JXUwMDExJXUwMDFk of each angle is a vertex of the triangle.

Triangles can be classified by their angles. In doing so, it must be realized that all triangles have at least two JXUwMDM5JXUwMDAyJXUwMDE2JXUwMDAxJXUwMDEx angles, and that we classify the triangle according to the third angle which is either JXUwMDM5JXUwMDAyJXUwMDE2JXUwMDAxJXUwMDEx , JXUwMDM3JXUwMDBkJXUwMDE2JXUwMDAxJXUwMDA2JXUwMDE2 , or JXUwMDJhJXUwMDFiJXUwMDBlJXUwMDBmJXUwMDFj .

Triangles can also be classified by their JXUwMDJiJXUwMDFhJXUwMDBkJXUwMDAxJXUwMDE2 .

A triangle that has no congruent sides is classified as: JXUwMDJiJXUwMDEwJXUwMDAyJXUwMDBkJXUwMDA5JXUwMDBiJXUwMDBi

A triangle that has at least two congruent sides is classified as: JXUwMDMxJXUwMDFhJXUwMDFjJXUwMDFjJXUwMDEwJXUwMDA2JXUwMDA5JXUwMDA5JXUwMDE2

A triangle that has three congruent sides is classified as: JXUwMDNkJXUwMDE0JXUwMDA0JXUwMDFjJXUwMDA1JXUwMDBkJXUwMDE1JXUwMDExJXUwMDE3JXUw MDEzJXUwMDBk

Parts of an isosceles triangle:

The angle formed by the congruent sides is called the JXUwMDJlJXUwMDEzJXUwMDE3JXUwMDA2JXUwMDExJXUwMDFk JXUwMDM5JXUwMDBmJXUwMDA5JXUwMDBiJXUwMDA5 .

The side opposite the vertex angle is called the JXUwMDNhJXUwMDAzJXUwMDEyJXUwMDE2 .

In a JXUwMDJjJXUwMDA2JXUwMDEzJXUwMDBmJXUwMDFkJXUwMDFmJXUwMDBkJXUwMDE1JXUwMDFkJXUw MDA2JXUwMDAx , you slide a figure from one position to another without turning it.

In a reflection, you flip a figure over a JXUwMDM0JXUwMDA1JXUwMDA3JXUwMDBi . The new figure is a mirror image.

In a rotation, you turn a figure around a fixed JXUwMDI4JXUwMDFmJXUwMDA2JXUwMDA3JXUwMDFh . Rotations are sometimes called turns.

Refer to the figure to the right:   Each point on the preimage can be paired with exactly one point on its image, and each point on the image can be paired with exactly one point on the preimage. This one-to-one correspondence is an example of a JXUwMDM1JXUwMDBjJXUwMDExJXUwMDAwJXUwMDE5JXUwMDA3JXUwMDA5 .   Point M maps to point JXUwMDFl . Point JXUwMDA5 is the preimage of point J. Segment PN is the preimage of segment JXUwMDEwJXUwMDBm . This mapping is called a JXUwMDJjJXUwMDA2JXUwMDEzJXUwMDBmJXUwMDFkJXUwMDE1JXUwMDA5JXUwMDFkJXUwMDFmJXUw MDBjJXUwMDE1JXUwMDFkJXUwMDA2JXUwMDAx .