Congruent Shapes in Geometry

Questions and Answers

Three pairs of sides are congruent

Two pairs of sides and the angle between them are congruent

Two pairs of angles and the side between them are congruent

A pair of sides and the angle between them are congruent (correct)

Congruence refers to same shape and size, while equality refers to same position

Congruence and equality are interchangeable terms

Congruence refers to same position, while equality refers to same shape and size

Congruence accepts differences in position, while equality does not (correct)

Windows on an apartment building (correct)

Wheels on a car

Seats on a bus

Doors on a house

The hypotenuse and correspondent legs of each are congruent Signup and view all the answers

They are congruent but not equal Signup and view all the answers

They have sides of the same length and angles of the same measure Signup and view all the answers

Scaling Signup and view all the answers

One is a scaled version of the other Signup and view all the answers

SSS (Side-Side-Side) Signup and view all the answers

Congruent shapes are always similar, but similar shapes are not always congruent Signup and view all the answers

Study Notes

Two figures are congruent if they have the same shape and size, despite possible differences in position and orientation.
Congruent shapes have sides of the same length and angles of the same measure.

Translation: a shape can be slid to change its position without affecting its congruence.
Rotation: a shape can be turned at any angle without affecting its congruence.
Reflection: a shape can be flipped without affecting its congruence.

Similar shapes have the same angles but may have different sizes.
Congruent shapes are always similar, but similar shapes are not always congruent.
Resizing a similar shape can make it congruent.

SSS (Side-Side-Side): if all corresponding sides of two triangles are congruent, then the triangles are congruent.
SAS (Side-Angle-Side): if a pair of sides and the angle between them are congruent, then the triangles are congruent.
ASA (Angle-Side-Angle): if a pair of angles and the side between them are congruent, then the triangles are congruent.
AAS (Angle-Angle-Side): if a pair of angles and a side (not between the angles) are congruent, then the triangles are congruent.
HL (Hypotenuse-Leg): for right-angle triangles only, if the hypotenuse and corresponding legs are congruent, then the triangles are congruent.

Congruent figures can be transformed in relation to each other through translation, rotation, or reflection.
Congruent figures can be found in real-life applications, such as construction, where identical shapes and sizes are required.

Congruence and equality are not interchangeable terms in mathematics.
Equality implies that all properties are equal, while congruence accepts differences in position.

Incongruent figures have different shapes and sizes, and their pairs of sides and angles are not equal.
Incongruent figures cannot be made congruent by resizing or transforming them.