Geometry Unit 1: Constructions & Transformations

Questions and Answers

What is the purpose of a compass?

To find midpoints

To draw circles (correct)

To draw lines

To measure angles

What is a straightedge used for?

To draw circles

To measure distances

To draw lines (correct)

To shade areas

What defines perpendicular lines?

Lines that intersect to form 90° angles.

What are parallel lines?

Lines that never intersect. Signup and view all the answers

What does it mean to bisect?

To split into two equal sections. Signup and view all the answers

What is a perpendicular bisector?

A line that intersects to form 90° angles and splits the original segment into two equal sections. Signup and view all the answers

What is an equilateral triangle?

A triangle with three equal sides. Signup and view all the answers

Describe a square.

A quadrilateral with four equal sides and four 90° angles. Signup and view all the answers

What does congruent mean?

Same size and shape (equal). Signup and view all the answers

Define rigid transformations.

Movements of figures that preserve their size and shape. Signup and view all the answers

What is a pre-image?

The original figure. Signup and view all the answers

What is the image in geometry?

The figure after the transformation. Signup and view all the answers

What is rotation in geometry?

A turn with a given center, direction, and angle. Signup and view all the answers

What does reflection mean?

A flip across a line where reflected points cross in a perpendicular line and are equal distance from the line. Signup and view all the answers

Define translation in geometric terms.

A slide along a directed line segment with a given distance and direction. Signup and view all the answers

What is reflection symmetry?

If a figure lands onto itself after a reflection. Signup and view all the answers

What is rotational symmetry?

If a figure lands onto itself after a rotation. Signup and view all the answers

What are sequences of rigid transformations used for?

To carry figures onto one another and prove congruence. Signup and view all the answers

Define supplementary angles.

Two angles that are in a line so add to 180°. Signup and view all the answers

What are vertical angles?

Angles across from each other and congruent. Signup and view all the answers

What are corresponding angles?

Angles congruent when parallel lines are cut by a transversal and can be matched with a translation. Signup and view all the answers

What are alternate interior angles?

Angles congruent when parallel lines are cut by a transversal and can be matched with a rotation. Signup and view all the answers

What does the Triangle Angle Sum Theorem state?

The angles in any triangle sum to 180°. Signup and view all the answers

What is construction in geometry?

To draw a shape, line, or angle accurately using a compass and straightedge. Signup and view all the answers

Define a line segment.

A part of a line that has two endpoints. Signup and view all the answers

What is a circle?

A round figure whose boundary consists of points equidistant from the center. Signup and view all the answers

What is a radius?

The distance from the center of a circle to any point on the circle. Signup and view all the answers

What is an intersection in geometry?

A point where lines intersect. Signup and view all the answers

Define an angle.

A figure formed by two rays with a common endpoint. Signup and view all the answers

What is a vertex?

A corner point of an angle or figure. Signup and view all the answers

Study Notes

Tools for Construction

Compass: A tool for drawing circles.
Straightedge: Used for drawing straight lines.

Types of Lines

Perpendicular Lines: Intersect to form 90° angles.
Parallel Lines: Never intersect.

Definitions in Geometry

Bisect: The action of splitting an object into two equal parts.
Perpendicular Bisector: A line that is both perpendicular to a segment and bisects it.

Geometric Figures

Equilateral Triangle: All three sides are equal in length.
Square: A quadrilateral featuring four equal sides and four right angles.

Congruence

Congruent: Figures that are the same size and shape.
Rigid Transformations: Movements that maintain the size and shape of figures.

Images and Pre-images

Pre-image: The original figure before any transformations.
Image: The resulting figure after transformation.

Types of Transformations

Rotation: A turn around a fixed point, defined by center, direction, and angle.
Reflection: A flip over a line where points are equidistant from the line.
Translation: A slide along a directed line with specific distance and direction.

Symmetry

Reflection Symmetry: When a figure coincides with itself upon reflection.
Rotational Symmetry: When a figure matches its original position after a rotation.

Applications of Transformations

Sequences of Rigid Transformations: Used to superimpose figures for proving congruence.

Angle Properties

Supplementary Angles: Two angles on a straight line that add up to 180°.
Vertical Angles: Opposite angles formed by two intersecting lines, congruent in measure.
Corresponding Angles: Angles that are congruent when parallel lines are intersected by a transversal.
Alternate Interior Angles: Congruent angles formed on opposite sides of a transversal between two parallel lines.

Triangle Properties

Triangle Angle Sum Theorem: The sum of all interior angles of a triangle equals 180°.

Construction Methods

Construction: The precise drawing of lines, shapes, or angles using compass and straightedge.
Line Segment: A portion of a line defined by two endpoints.

Basic Geometry Concepts

Circle: A shape where all points are equidistant from the center.
Radius: The distance from the center of a circle to any point on its perimeter.
Intersection: The point where two lines cross.
Angle: Formed by two rays sharing a common endpoint.
Vertex: The point where two sides of an angle or figure meet.

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Explore key terms related to constructions and rigid transformations in geometry with these flashcards. Learn about essential tools like compass and straightedge, as well as concepts such as parallel and perpendicular lines. This quiz helps reinforce foundational geometry vocabulary.