PRE-GEOMETRY
CHAPTER 1: GEOMETRIC CONCEPTS
1.1 BASIC GEOMETRIC CONCEPTS
A. POINT, LINE AND PLANE
1. Introduction
2. Point
3. Line
4. Plane
5. Collinear Points
B. LINE SEGMENT, RAY AND HALF LINE
1. Line Segment
2. Ray
3. Half Line
C. PLANE AND SPACE
1. Plane
2. Space
D. RELATION BETWEEN TWO LINES
1. Intersecting Lines
2. Parallel Lines
3. Coincident Lines
4. Skew Lines
E. RELATION BETWEEN A LINE AND A PLANE
1. The Intersection of a Line and a Plane
2. Parallelism of a Line and a Plane
3. A Line Lies in a Plane
F. RELATION BETWEEN TWO PLANES
1. Parallel Planes
2. Intersecting Planes
3. Coincident Planes
4. Half Planes
CHAPTER 2: ANGLES
2.1 ANGLES
A. REGIONS OF AN ANGLE
1. Angle
2. Interior and Exterior Regions of an Angle
B. MEASURING ANGLES
C. TYPES OF ANGLE WITH RESPECT TO THEIR MEASURES
1. Acute Angle
2. Right Angle
3. Obtuse Angle
4. Straight Angle
5. Complete Angle
D. TYPES OF ANGLE WITH RESPECT TO THEIR POSITION
1. Adjacent Angles
2. Vertical Angles
3. Congruent Angles
E. TYPES OF ANGLE WITH RESPECT TO THE SUM OF THEIR MEASURES
1. Complementary Angles
2. Supplementary Angles
2.2 ANGLES FORMED BY A TRANSVERSAL
A. CORRESPONDING ANGLES AND ALTERNATE ANGLES
1. Corresponding Angles
2. Alternate Interior Angles
3. Alternate Exterior Angles
4. Interior Angles on the Same Side of a Transversal
5. Angles with Parallel Sides
6. Bisector of an Angle
CHAPTER 3: TRIANGLES
3.1 TRIANGLES
A. BASIC CONCEPTS
1. Definition
2. Angles of a Triangle
3. Interior and Exterior Regions of a Triangle
4. Intersection of a Triangle and a Line
B. TYPES OF TRIANGLE
1. Triangle Types Defined by Sides
2. Triangle Types Defined by Angles
C. PROPERTIES OF THE ANGLES AND SIDES OF A TRIANGLE
1. Angles of a Triangle
2. Relations Between the Angles and the Sides of a Triangle
3.2 CONGRUENT AND SIMILAR TRIANGLES
A. CONGRUENT TRIANGLES
1. Concept of Congruence and Congruent Triangles
2. Proving that Triangles are Congruent
B. SIMILAR TRIANGLES
1. Concept of Similarity
2. Similar Triangles
3. Proving that Triangles are Similar
4. Examples and Applications
3.3 CONSTRUCTING TRIANGLES
1. Constructing a Triangle from Three Known Sides
2. Constructing a Triangle From Two Known Angles and a Known Side
3. Constructing Triangle From Two Known Sides and a Known Angle
3.4 RIGHT TRIANGLES
1. The Pythagorean Theorem
2. Isosceles Right Triangles (45°-45°-90° Triangles)
3. 30°-60°-90° Right Triangles
4. The Euclidean Theorems
3.5 PERIMETER AND AREA OF A TRIANGLE
1. Perimeter of a Triangle
2. Area of a Triangle
CHAPTER 4: POLYGONS
4.1 POLYGONS
A. POLYGONS AND THEIR PROPERTIES
1. Introducing Polygons
2. Convex and Concave Polygons
3. Types of Polygon
4. Regular Polygons
5. Diagonals of a Polygon
B. ANGLES OF A POLYGON
1. Interior Angles of a Polygon
2. Exterior Angles of a Polygon
4.2 QUADRILATERALS
1. Definition
2. Angles of a Quadrilateral
4.3 TYPES OF QUADRILATERAL
A. PARALLELOGRAM
1. Properties of a Parallelogram
2. Perimeter of a Parallelogram
3. Area of a Parallelogram
B. RECTANGLE
1. Perimeter of a Rectangle
2. Area of Rectangle
C. SQUARE
1. Perimeter of a Square
2. Area of a Square
D. RHOMBUS
1. Perimeter of a Rhombus
2. Area of a Rhombus
E. KITE
1. Perimeter of a Kite
2. Area of a Kite
F. TRAPEZOID
1. Definition
2. Properties of a Trapezoid
3. Isosceles Trapezoid
4. Right Trapezoid
5. Perimeter of a Trapezoid
6. Area of a Trapezoid
CHAPTER 5: CIRCLES
5.1 CIRCLES
A. BASIC CONCEPTS
1. Definition
2. Regions Separated by a Circle in a Plane
3. Auxiliary Elements of a Circle
4. Relative Position of a Line and a Circle in the Same Plane
B. CHORDS
C. TANGENTS
D. RELATIVE POSITION OF TWO CIRCLES IN THE SAME PLANE
5.2 ARCS AND ANGLES OF A CIRCLE
A. ARCS AND CENTRAL ANGLES
B. INSCRIBED ANGLES
5.3 CIRCUMFERENCE AND AREA OF A CIRCLE
A. CIRCUMFERENCE AND ARC LENGTH
1. Circumference of a Circle
2. Arc Length
B. AREA OF A CIRCLE, A SECTOR AND A SEGMENT
1. Area of a Circle
2. Area of an Annulus
3. Area of a Sector
4. Area of a Segment
5.4 BASIC CONSTRUCTIONS
CHAPTER 6: TRIGONOMETRY
6.1 TRIGONOMETRIC RATIOS IN A RIGHT TRIANGLE
A. TRIGONOMETRIC RATIOS OF ACUTE ANGLES
B. RECIPROCAL TRIGONOMETRIC RATIOS
C. TRIGONOMETRIC RATIOS OF COMPLEMENTARY ANGLES
D. BASIC TRIGONOMETRIC IDENTITIES
E. FINDING A TRIGONOMETRIC RATIO FROM A GIVEN RATIO
6.2 TRIGONOMETRIC RATIOS OF SOME SPECIAL TRIANGLES
A. RATIOS IN 30°-60°-90° TRIANGLE
B. RATIOS IN 45°-45°-90° TRIANGLE
6.3 USING A TRIGONOMETRIC TABLE
1. Using a Table of Trigonometric Ratios
2. The Ranges of Sine and Cosine
6.4 APPLICATIONS OF TRIGONOMETRY
CHAPTER 7: MEASUREMENTS
7.1 MEASUREMENTS
A. BASIC CONCEPTS
B. MEASUREMENTS OF LENGTH
1. Metric Units of Length
2. Converting Units of Length
C. MEASUREMENTS OF AREA
1. Metric Units of Area
2. Converting Units of Area
3. Measuring Land Area
D. MEASUREMENTS OF VOLUME
1. Metric Units of Volume
2. Converting Units of Volume
3. Prisms
4. Volume and Surface Area of Some Common Solids
E. MEASUREMENTS OF CAPACITY AND MASS
1. Metric Units of Capacity
2. Metric Units of Mass
F. MEASUREMENTS OF TIME
1. Units of Time