About This Chapter
Introduction to Geometric Figures - Chapter Summary and Learning Objectives
You can build a solid foundation of geometric knowledge with these introductory lessons. Become familiar with the essential basic terms and concepts while making geometric constructions with a variety of tools. Learn about the various types of lines and angles as you delve deeper into the world of geometry. This chapter can help you understand the following:
- Measurement of line segments
- Geometric constructions using various tools and methods
- Copying of line segments and angles
- Line segment bisections
- Parallel, perpendicular and transversal lines
- Construction of lines
- Types of angles: vertical, corresponding, alternate interior, alternate exterior and consecutive interior
- Angle bisectors
- Construction of squares, equilateral triangles and regular hexagons inscribed in circles
|Line Segments and Rays||Define line segment and ray. Explain how to measure the distance of a line segment as well as how to find the length of a segment that is made up of other segments. Become familiar with the Segment Addition Postulate.|
|Points, Lines, and Angles in Geometry||Define basic vocabulary surrounding geometry: point, types of lines, degrees and right angle.|
|Make Geometric Constructions with Tools||Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).|
|Practice Making Geometric Constructions with Tools||Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).|
|Geometric Constructions Using Lines and Angles||Define geometric construction. Demonstrate how to use construction to copy a line segment and then do the same for an angle.|
|Line Segment Bisection and Midpoint Postulate||Demonstrate how to use construction to bisect a segment. Show midpoint of a given line segment.|
|Parallel, Perpendicular and Transverse Lines||Learn the definitions of parallel, perpendicular, and transversal lines.|
|Constructing Perpendicular Lines||Demonstrate how to construct perpendicular lines. Construct a line perpendicular to a given line passing through a given point not on that line.|
|Types of Angles: Vertical, Corresponding, Alternate Interior and Others||Learn the definitions of vertical, corresponding, alternate interior, alternate exterior and consecutive interior angles.|
|Constructing an Angle Bisector||Define an angle bisector. Demonstrate how to construct an angle bisector by using a compass and straightedge to bisect an angle.|
|Constructing Equilateral Triangles, Squares, and Regular Hexagons Inscribed in Circles||Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.|
1. Line Segments & Rays: Definition & Measurement
Watch this video lesson to learn the difference between a line segment and a ray. You will also learn how to measure and add line segments. Learn why you can't measure or add a ray.
2. Types of Angles: Vertical, Corresponding, Alternate Interior & Others
In addition to basic right, acute, or obtuse angles, there are many other types of angles or angle relationships. In this lesson, we will learn to identify these angle relationships and discuss their measurements.
3. Geometric Constructions Using Lines and Angles
Watch this video lesson to learn about geometric construction and how you can copy line segments and angles without using any numbers. All you need is a straight edge and a compass.
4. Line Segment Bisection & Midpoint Theorem: Geometric Construction
Watch this video lesson and you will learn how to bisect a line segment without measurements using just a compass and a straight edge. You'll also learn about the midpoint theorem, which lets you calculate the midpoint if you have the measurements.
5. Dividing Line Segments into Equal Parts: Geometric Construction
Watch this video lesson to learn one way to easily divide any line segment into as many equal parts as you need. Also, learn where in real life this skill comes in handy.
6. Parallel, Perpendicular and Transverse Lines
What are the different types of lines? Where are they visible in the real world and how can you recognize them? Find out here and test your knowledge with a quiz.
7. Constructing Perpendicular Lines in Geometry
In this video lesson, you will see how to use geometric construction to draw perpendicular lines. Learn why geometric construction is useful. Also find out the only two tools in addition to your pencil that you need to do this.
8. Constructing an Angle Bisector in Geometry
Watch this video lesson to learn a cool way to split an angle in half. You can use this method to split a pie slice in half where you can be sure each side is equal.
9. Methods & Tools for Making Geometric Constructions
Did you know that it's possible to do math without using numbers? This is exactly what Euclid did when he showed how to solve mathematical problems by drawing them out instead of with numbers.
10. Practice Making Geometric Constructions with Tools
There are a number of tools available to geometry students to help make their work a bit easier. In this lesson, we will review how to use many of them in order for you to get the most out of every geometry class.
11. Constructing Equilateral Triangles, Squares, and Regular Hexagons Inscribed in Circles
Constructing an accurate triangle, square, or hexagon within a circle is a matter of a few simple steps, and can be extremely practical. In this lesson, we'll practice the construction of those three shapes.
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Other chapters within the Geometry: High School course
- High School Geometry: Foundations of Geometry
- High School Geometry: Logic in Mathematics
- High School Geometry: Properties of Triangles
- High School Geometry: Triangles, Theorems and Proofs
- High School Geometry: Parallel Lines and Polygons
- High School Geometry: Similar Polygons
- High School Geometry: Quadrilaterals
- High School Geometry: Circular Arcs and Circles
- High School Geometry: Conic Sections
- High School Geometry: Geometric Solids
- High School Geometry: Analytical Geometry
- High School Geometry: Probability
- High School Geometry: Introduction to Trigonometry