Geometry Midterm Review

Study Notes

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.