Enhance Your Learning with Congruence and Similarity Flash Cards for quick learning
Figures that have the same shape and size, denoted by the symbol ≅.
Figures that have the same shape but not necessarily the same size, denoted by the symbol ~.
Transformations that preserve the shape and size of a figure, such as translations, rotations, and reflections.
Transformations that preserve the shape of a figure but not necessarily the size, such as dilations.
Conditions or rules that determine when two figures are congruent, such as side-side-side (SSS), side-angle-side (SAS), and angle-side-angle (ASA).
Conditions or rules that determine when two figures are similar, such as angle-angle (AA), side-side-side (SSS), and side-angle-side (SAS).
Relationships between corresponding sides or corresponding angles of similar figures, where the ratios are equal.
The study of similar triangles and their properties, including the proportionality of corresponding sides and the equality of corresponding angles.
Logical arguments that use congruence and similarity criteria to prove the equality or proportionality of sides and angles in geometric figures.
Real-world situations where congruence and similarity concepts are used to solve problems, such as scaling objects, map navigation, and architectural design.
The sides and angles of congruent or similar figures that occupy the same relative positions.
The ratio of corresponding lengths of two similar figures.
If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
If the corresponding sides of two triangles are congruent, then the triangles are congruent.
If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
If a ray bisects an angle of a triangle, then it divides the opposite side into segments that are proportional to the other two sides.
If a line parallel to one side of a triangle intersects the other two sides, then it divides those sides proportionally.
If an angle of one triangle is congruent to an angle of another triangle and the lengths of the sides including these angles are proportional, then the triangles are similar.
If the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar.
If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
A transformation that changes the size of a figure without changing its shape, using a scale factor.
The fixed point in a dilation where all points are either expanded or contracted from.
The ratio of the lengths of corresponding sides in a dilation.
Polygons that have the same shape but not necessarily the same size.
Polygons that have the same shape and size.
Corresponding sides or corresponding segments of similar figures that are in proportion.
The ratio of the areas of two similar figures is equal to the square of the ratio of their corresponding side lengths.
The ratio of the volumes of two similar three-dimensional figures is equal to the cube of the ratio of their corresponding side lengths.
The positive square root of the product of two numbers.
In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
The ratio of the lengths of corresponding sides in similar figures.
A transformation that produces similar figures.
A transformation that produces congruent figures.
A line or ray that divides an angle into two congruent angles.
A line, segment, or ray that is perpendicular to a segment at its midpoint.
A perpendicular segment from a vertex of a triangle to the line containing the opposite side.
A segment from a vertex of a triangle to the midpoint of the opposite side.
The point of concurrency of the medians of a triangle.
The point of concurrency of the altitudes of a triangle.
The point of concurrency of the perpendicular bisectors of the sides of a triangle.
The point of concurrency of the angle bisectors of a triangle.
A statement that indicates two figures are similar, usually written using the symbol ~.
A statement that indicates two figures are congruent, usually written using the symbol ≅.