Planar Geometry: Points, Lines, and Figures

Planar Geometry: Points, Lines, and Figures

Planar Geometry: Points and Lines

Points: A location in space, represented by a dot and labeled with a capital letter.
Lines: Straight paths that extend infinitely in both directions. Named with two points or a lowercase letter.
Line Segments: Part of a line with two endpoints.
Rays: Part of a line with one endpoint, extending infinitely in one direction.

Measuring Angles

Angles are formed by two rays (sides) with a common endpoint (vertex).
Measured in degrees (°) using a protractor.

Types of Angles

Acute angle: < 90°
Right angle: = 90°
Obtuse angle: > 90° and < 180°
Straight angle: = 180°
Reflex angle: > 180° and < 360°

Triangles

Equilateral: All sides and angles equal
Isosceles: Two sides and two angles equal
Scalene: No sides or angles equal
Right triangle: Has one right angle
Triangle Sum: Angles add up to 180°

Quadrilaterals

Parallelogram: Opposite sides parallel
Rectangle: Parallelogram with 4 right angles
Square: Rectangle with all sides equal
Rhombus: Parallelogram with all sides equal
Trapezoid: At least one pair of parallel sides
Angles Sum: 360°

Polygons

Closed shape with 3 or more straight sides
Regular: All sides and angles equal
Sum of angles: (n-2) × 180°, where n = number of sides

Circles

Set of points equidistant from a center
Radius: Center to edge
Diameter: Edge through center to opposite edge (2 × radius)
Circumference: Distance around (C = 2πr)
Arc, chord, sector: Parts of a circle

Solid Figures

Cube, Rectangular Prism, Cylinder, Sphere, Pyramid, Cone
Properties: Faces, edges, vertices

Surface Area

Sum of the areas of all faces of a solid
Cube: 6a²; Rectangular prism: 2(lw + lh + wh)
Cylinder: 2πr² + 2πrh

Graphing Figures

Plotting points on a coordinate plane (x, y)
Measuring distances using the distance formula
Finding midpoints, slopes, and equations of lines

Examples

Points and Lines: Plot points A(2, 3) and B(7, 3). Draw line AB.
Line Segment: If AB = 5 units, and A is at (2,3), what are possible coordinates for B?
Measuring Angles: If ∠ABC = 65°, what type of angle is it? (Acute)
Types of Angles: Name angle of 110°. (Obtuse)
Triangle: A triangle has angles 50°, 60°, and ___. Find the missing angle. (70°)
Quadrilateral: Rectangle sides are 5 cm and 8 cm. Area = ___? (40 cm²)
Polygon: What is the sum of angles in a pentagon? (540°)
Circle: Circle with radius 6 cm. Circumference = ___? (12π cm)
Solid Figure: Cube with edge 4 cm. Surface area = ___? (96 cm²)
Graphing: Find the midpoint between (2,5) and (6,9). ((4,7))

Pre-Test (40 Questions)

Questions & Answers (Based on Your Pre-Test)

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Post-Test (40 Questions)