Geometry Midterm Review

Geometry Midterm Review

• Basic Geometric Figures:

  • Point: A location in space.
  • Line: A straight path extending infinitely in two directions.
  • Plane: A flat surface extending infinitely in all directions.
  • Ray: A part of a line with one endpoint that extends infinitely in one direction.
  • Segment: A part of a line with two endpoints.
  • Collinear: Points that lie on the same line.

• Angles:

  • Angle: Formed by two rays with a common endpoint.
  • Acute Angle: An angle less than 90 degrees.
  • Right Angle: An angle equal to 90 degrees.
  • Obtuse Angle: An angle greater than 90 degrees but less than 180 degrees.
  • Straight Angle: An angle equal to 180 degrees.
  • Supplementary Angles: Two angles whose measures add up to 180 degrees.
  • Complementary Angles: Two angles whose measures add up to 90 degrees.
  • Linear Pair: Two adjacent angles that form a straight line.
  • Vertical Angles: A pair of opposite angles made by intersecting lines.

• Triangles:

  • Isosceles Triangle: A triangle with at least two congruent sides.
  • Scalene Triangle: A triangle with no congruent sides.
  • Equilateral Triangle: A triangle with all three sides congruent.
  • Right Triangle: A triangle with one right angle.
  • Obtuse Triangle: A triangle with one obtuse angle.
  • Equiangular Triangle: A triangle with all three angles congruent.

• Circle:

  • Center: The point in the middle of a circle.
  • Radius: A line segment from the center of a circle to a point on the circle.
  • Diameter: A line segment that passes through the center of a circle and has endpoints on the circle.
  • Chord: A line segment with endpoints on the circle.

• Geometric Proofs:

  • Undefined Terms: Point, line, and plane.
  • Two-Column Proof: A deductive argument organizing statements and reasons in two columns.
  • Properties of Equality:
    • Addition Property
    • Subtraction Property
    • Multiplication Property
    • Division Property
    • Distributive Property
    • Reflexive Property
    • Symmetric Property
    • Transitive Property
    • Substitution Property

• Transformation Conjectures:

  • Midpoint: A point that divides a segment into two congruent segments.
  • Congruent Figures: Figures with the same size and shape.
  • Bisect: To divide into two equal or congruent parts.
  • Bisector of an Angle: A ray that divides an angle into two congruent angles.

• Parallel and Perpendicular Lines:

  • Parallel Lines: Lines that never intersect.
  • Transversal: A line that intersects two or more lines.
  • Same-Side Interior Angles: Interior angles on the same side of the transversal.
  • Alternate Interior Angles: Interior angles on opposite sides of the transversal.
  • Alternate Exterior Angles: Exterior angles on opposite sides of the transversal.
  • Corresponding Angles: Angles in the same position relative to the transversal.
  • Perpendicular Lines: Lines that intersect to form right angles.
  • Perpendicular Bisector: A line that is perpendicular to a segment at its midpoint.

• Geometric Transformations:

  • Transformation: A change in the position, size, or orientation of a figure.
  • Pre-image: The original figure before a transformation.
  • Image: The figure after a transformation.
  • Rigid Motion: A transformation that preserves size and shape.
  • Translation: A transformation that slides a figure in a given direction and distance.
  • Directed Line Segment: The distance and direction of a translation.
  • Rhombus: A quadrilateral with all four sides congruent.
  • Reflection: A transformation that flips a figure over a line.
  • Line of Reflection: The line over which a figure is reflected.
  • Reflectional Symmetry: A figure that can be reflected across a line and remain unchanged.
  • Line of Symmetry: A line that divides a figure into two mirror images.
  • Rotation: A transformation that turns a figure around a point.
  • Rotational Symmetry: A figure that can be rotated around a point and remain unchanged.
  • Angle of Rotational Symmetry: The smallest angle of rotation that maps a figure onto itself.

• Congruency:

  • Congruent: Having the same size and shape.
  • Corresponding Parts: Parts of congruent figures that are in the same positions.
  • CPCTC: Corresponding Parts of Congruent Triangles are Congruent.
  • Triangle Congruence Criteria: Shortcuts to determine if two triangles are congruent
    • SSS (Side-Side-Side)
    • SAS (Side-Angle-Side)
    • ASA (Angle-Side-Angle)
    • AAS (Angle-Angle-Side)
    • HL (Hypotenuse-Leg)

• Theories

  • Triangle Sum Theorem: The sum of the angles in a triangle is 180°.
  • Auxiliary Line: A line temporarily added to a diagram to help in a proof.
  • Isosceles Triangle Theorem: If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

• Counterexample: An example or case that proves a conjecture or theory wrong.

Prepare for your Geometry midterm with this comprehensive review quiz focusing on basic geometric figures and angles. Test your understanding of essential concepts such as points, lines, angles, and their classifications. This quiz will help solidify your knowledge and boost your confidence before the exam.