About This Chapter
Geometric Properties of Objects - Chapter Summary
This chapter explores the properties of various shapes, including triangles, circles, rectangles, trapezoids and parallelograms. You will examine similar triangles and learn about different types of lines. Other lessons cover angles, and one lesson consists of practice problems to let you improve your skills in solving problems with angle pairs. Objectives covered in these lessons include:
- Parallel, perpendicular and transverse lines
- Vertical, corresponding, alternate interior and other types of angles
- The Pythagorean Theorem and its applications
- Properties of quadrilaterals, parallelograms, trapezoids and polygons
- Properties of congruent and similar shapes
- Applying scale factors to perimeter, area and volume of similar figures
Experienced instructors will guide you through each topic in these engaging video lessons, using real-world examples to show you how these concepts work. You can use the self-assessment quizzes at the end of each lesson to test your knowledge. Feel free to watch the videos as many times as you'd like.
Geometric Properties of Objects Chapter Objectives
Many first-time students to the California State University system must take the ELM exam to determine their placement in mathematics courses. The ELM has a 90-minute time limit. It contains 50 multiple-choice questions, divided into three sections. The material covered in this chapter's lessons is in the Geometry section, which makes up about 30% of the total test.
1. Properties of Shapes: Rectangles, Squares and Rhombuses
What's the difference between a square and a rectangle? What about a rhombus and a square? In this lesson, we'll look at the properties of these shapes.
2. Properties of Shapes: Quadrilaterals, Parallelograms, Trapezoids, Polygons
Four-sided objects are more than just squares and rectangles. In this lesson, we'll discuss quadrilaterals, parallelograms and trapezoids. We'll also discuss polygons, objects that can have more sides than you can count.
3. Properties of Congruent and Similar Shapes
In this lesson, we'll look at triangles, rectangles and other shapes that share properties. This includes both congruent and similar shapes. We'll also practice identifying the missing properties of these shapes.
4. Applying Scale Factors to Perimeter, Area, and Volume of Similar Figures
How do shapes change sizes yet retain their proportions and similarities to other shapes? In this lesson, we'll look at what a scale factor is and how to apply it. We'll consider scale factors with regards to three different aspects of similar shapes: perimeter, area and volume.
5. Angles and Triangles: Practice Problems
Want more practice solving with angle pairs? How about more review for solving angles in triangles? Look no further. Get more practice here, and test your ability with a quiz.
6. The Pythagorean Theorem: Practice and Application
The Pythagorean theorem is one of the most famous geometric theorems. Written by the Greek mathematician Pythagoras, this theorem makes it possible to find a missing side length of a right triangle. Learn more about the famous theorem here and test your understanding with a quiz.
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Other chapters within the Basic Geometry: Help & Review course
- Introduction to Basic Geometry
- Geometry Topics
- Basic Geometry: Lines & Angles
- Basic Geometry: Polygons
- Basic Geometry: Triangles
- Basic Geometry: Quadrilaterals
- Basic Geometry: Circles
- Basic Geometric Constructions
- Basic Geometry: Similar Figures
- Basic Geometry: Perimeter, Circumference & Area
- Basic Geometry: 3-Dimensional Figures
- Lines and Angles in Geometry
- Perimeter, Area & Volume
- Geometric Graphing Basics
- Geometric Graphing Functions