"two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other."
Congruent shapes have the same size and shape, and this topic covers how to determine if two shapes are congruent, the different types of congruence (such as side-angle-side and angle-side-angle), and how to use congruence to solve problems.
Basic concepts of geometry: These include points, lines, angles, planes, and their properties that are essential in understanding congruence.
Congruent figures: Two figures are said to be congruent if they have the same shape and size. This concept is fundamental in understanding congruence in geometry.
Congruence criteria: There are various criteria that can be used to determine if two figures are congruent, such as side-side-side, angle-angle-side, and side-angle-side.
Properties of congruent figures: Understanding the properties of congruent figures helps in solving problems involving transformations, proofs, and similarity.
Congruent triangles: The concepts involved in proving triangles are congruent using different criteria, such as the SAS, ASA, and SSS criteria.
Transformations: Understanding transformations like reflections, rotations, and translations can help to visualize and understand the effects of congruence.
Congruence in circles: Understanding how to prove congruence in circles using chords, secants, and tangents.
Congruent models: Using physical models to represent congruent figures or to show a transformation of one congruent figure to another.
Constructions: Understanding how to construct congruent figures using a ruler and a compass or other available tools.
Real-world applications: Using congruence concepts in practical applications, such as in construction, architecture, and design.
Congruent angles: Two angles with the same measure.
Congruent segments: Two line segments with the same length.
Congruent triangles: Two triangles with the same shape and size.
Congruent circles: Two circles with the same size and shape.
Congruent polygons: Two polygons with the same shape and size.
Congruent quadrilaterals: Two quadrilaterals with the same shape and size.
Congruent rectangles: Two rectangles with the same shape and size.
Congruent squares: Two squares with the same shape and size.
Congruent parallelograms: Two parallelograms with the same shape and size.
Congruent trapezoids: Two trapezoids with the same shape and size.
Congruent rhombuses: Two rhombuses with the same shape and size.
Congruent kites: Two kites with the same shape and size.
Congruent regular polygons: Two regular polygons with the same shape and size.
Congruent lines: Two lines that are identical in length, orientation, and position.
Congruent planes: Two planes with the same size and shape.
Congruent 3D figures: Two 3D figures with the same size and shape.
"one can be transformed into the other by an isometry, i.e., a combination of rigid motions, namely a translation, a rotation, and a reflection."
"either object can be repositioned and reflected (but not resized) so as to coincide precisely with the other object."
"if they can be cut out and then matched up completely."
"a translation, a rotation, and a reflection."
"The word equal is often used in place of congruent for these objects."
"they have the same length."
"they have the same measure."
"they have the same diameter."
"their corresponding sides and angles, but also their corresponding diagonals, perimeters, and areas."
"the concept of similarity applies if the objects have the same shape but do not necessarily have the same size."
"Most definitions consider congruence to be a form of similarity."
"the objects have different sizes in order to qualify as similar."