Planar Geometry: Points and Lines

• Point: An exact location in space, no size or dimension.
• Line: Extends infinitely in both directions, has length but no thickness.

Line Segments and Rays

• Line Segment: Part of a line with two endpoints.
• Ray: Has one endpoint, extends infinitely in one direction.

Measuring Angles

• Angle: Formed by two rays meeting at a vertex.
• Measured in degrees (°) with a protractor.

Types of Angles

• Acute: Less than 90°
• Right: Exactly 90°
• Obtuse: More than 90° but less than 180°
• Straight: 180°
• Reflex: More than 180° but less than 360°

Triangles

• Types by sides: Equilateral (all equal), Isosceles (two equal), Scalene (none equal).
• Types by angles: Acute (all <90°), Right (one 90°), Obtuse (one >90°).
• Sum of angles: 180°

Quadrilaterals

• Has 4 sides.
• Examples: Square, Rectangle, Parallelogram, Rhombus, Trapezoid.
• Sum of angles: 360°

Polygons

• Closed figures with 3 or more straight sides.
• Regular: all sides and angles equal.
• Sum of angles: (n-2)×180° (n = number of sides)

Circles

• Set of points equidistant from a center.
• Parts: radius, diameter, chord, arc, sector, tangent.
• Area: πr². Circumference: 2πr.

Solid Figures

• 3D shapes: Cube, Cuboid, Sphere, Cylinder, Cone, Pyramid, Prism.
• Have volume and surface area.

Surface Area

• Sum of areas of all faces of a 3D object.
• Cube: 6a², Sphere: 4πr², Cylinder: 2πr(h+r).

Graphing Figures

• Placing points and shapes on coordinate plane (x, y).
• Distance between two points: √[(x2-x1)² + (y2-y1)²]

Explained Concepts

• Parallel Lines: Never meet, always same distance apart.
• Perpendicular Lines: Meet at 90° angle.
• Congruent Figures: Same size and shape.
• Similar Figures: Same shape, different size (proportional sides, equal angles).
• Transversal: A line that crosses two or more lines, forming angles.
• Diagonal: A line joining non-adjacent vertices of a polygon.

Examples

1. Sum of angles in a hexagon: (6-2)×180° = 720°
2. Area of triangle (base=6, height=9): ½×6×9 = 27
3. Area of circle (radius=4): π×4² = 16π ≈ 50.27
4. Distance between (1,2) and (4,6): √[(4-1)² + (6-2)²] = √(9+16) = 5
5. Volume of cube (side=3): 3³ = 27
6. Surface area of cylinder (r=2, h=5): 2π×2×(2+5) = 28π ≈ 87.96
7. Identify the diameter in a circle diagram: Line through center, touching both points on circle.
8. What is a sector: Region bounded by two radii and an arc.
9. Area of rectangle (l=8, w=3): 8×3 = 24
10. Diagonals in a pentagon: 5×2/2 = 5

Pre-Test (40 MCQs)

Questions and Answers (from your last Pre-Test)

Post-Test (40 MCQs)