Unit 3 Exploring Congruence

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Questions and Answers

What is the result of applying a reflection to a geometric figure?

The figure translates along a line.

The figure changes size.

The figure remains congruent to its preimage. (correct)

The figure rotates around a point.

Which of the following best describes a rotation?

A transformation that turns the figure around a fixed point. (correct)

A movement that slides the figure along a straight path.

A reflection that creates a mirror image of the figure.

A transformation that flips the figure over a line.

How do you determine the angle of rotation for a figure to map onto itself?

By measuring the distance between the preimage and image.

By identifying lines of symmetry in the figure. (correct)

By examining the shape of the figure and its congruent angles.

By determining the orientation of the figure after a transformation.

What type of transformation is a translation?

A sliding movement without rotation or reflection. Signup and view all the answers

What can be concluded when two figures are congruent?

They have the same size and shape. Signup and view all the answers

Which statement about congruence properties is true?

Translations ensure that figures remain the same size and shape. Signup and view all the answers

What defines a line of reflection for a figure?

A boundary that divides the figure into two equal parts. Signup and view all the answers

When using congruence statements, what is essential to include?

The corresponding angles and sides of the figures. Signup and view all the answers

What is the relationship between corresponding sides and angles in determining the congruence of two figures?

They must match in length and degree respectively. Signup and view all the answers

Which transformation does not change the size of a figure?

Reflection Signup and view all the answers

Which of the following is a characteristic of rigid motion transformations?

They maintain the shape and size of the figures. Signup and view all the answers

What is used to represent transformations in the coordinate plane?

Function notation Signup and view all the answers

Which statement best describes the criteria for triangle congruence?

Two triangles are congruent if they can be transformed into each other via rigid motions. Signup and view all the answers

What is a direct application of the concept of congruency in geometry?

Proving relationships between different geometric figures. Signup and view all the answers

Which of the following transformations would change the position of a figure but not its orientation?

Translation along a vector Signup and view all the answers

Which of the following statements about congruence is false?

Congruent figures can have different sizes. Signup and view all the answers

Study Notes

Geometry Concepts & Connections: Exploring Congruence

G.GSR.3.1: Focuses on understanding transformations like translations (sliding), rotations (turning), and reflections (flipping) to understand symmetry and congruence.
- Preimage: The original shape before a transformation
- Image: The transformed shape after a transformation.
- Symmetry: A figure has symmetry if it can be mapped onto itself by a transformation.
  - Line Symmetry: A figure has line symmetry if it can be folded in half so that the two halves match.
  - Rotational Symmetry: A figure has rotational symmetry if it can be rotated less than 360 degrees onto itself.
G.GSR.3.2: Investigates how these rigid motions (translations, rotations, reflections) preserve size and shape, leading to congruence.
- Rigid Motions: Transformations that keep the size and shape of a figure unchanged.
- Congruence: Two figures are congruent if they have the same size and shape.
- Congruence Statements: Statements that indicate which parts of congruent figures correspond.
G.GSR.3.3: Explores how transformations affect figures, specifically looking at the relationship between the initial figure (preimage) and the transformed one (image).
- Corresponding Parts: Matching sides and angles in congruent figures.
- Function Notation: A way to represent transformations using mathematical expressions, especially in coordinate geometry.
G.GSR.3.4: Applies understanding of congruence to solve problems, including proofs and missing measurements.
- Criteria for Triangle Congruence: Specific conditions that guarantee two triangles are congruent, helping solve geometric problems.
- Proofs: Logical arguments used to demonstrate the validity of mathematical statements.
  - Two-Column Proof: A type of proof using statements and corresponding reasons in columns.
  - Flow Proof: A proof that uses arrows to show the logical flow of the argument.