About This Chapter
Geometric Properties of Shapes - Chapter Summary
With the video lessons and quizzes in this chapter, you'll get a solid understanding of geometrical shapes and their properties. The Pythagorean Theorem and its use in determining distance are covered in this chapter, and another lesson explains how to use geometry in exploring mathematical situations. Topics covered in these lessons on geometric properties include:
- Properties of triangles, rectangles and circles
- Properties of quadrilaterals, trapezoids, parallelograms and polygons
- Properties of congruent and similar shapes
- How to identify similar triangles
- Applications of similar triangles
- The practice and application of the Pythagorean Theorem
- Using the Pythagorean Theorem to find distance
- Analyzing mathematical situations using symmetry and transformations
In each engaging video lesson, you'll learn about these geometric principles and how to use them in preparing for the test. The self-assessment quizzes that accompany each lesson allow you to analyze your knowledge and also become acquainted with the types of questions you could see on your 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. How to Identify Similar Triangles
Similar triangles have the same characteristics as similar figures but can be identified much more easily. Learn the shortcuts for identifying similar triangles here and test your ability with a quiz.
5. Applications of Similar Triangles
Similar triangles are used to solve problems in everyday situations. Learn how to solve with similar triangles here, and then test your understanding 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.
7. Finding Distance with the Pythagorean Theorem
How much faster is it to cut the corners in a race around the block? In this lesson, review the Pythagorean Theorem, and figure out how to solve without a right triangle.
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Other chapters within the Math Review for Teachers: Study Guide & Help course
- Fundamental Number Concepts
- Operation Properties & Computation
- Ratios, Proportions and Percents
- Numerical Reasoning
- Equations and Inequalities
- Coordinate Geometry Concepts & Practice Problems
- Systems of Measurement
- Measurement & Scaling for Simple & Complex Figures
- Data Analysis & Visualization
- Probability Concepts & Calculations