About This Chapter
CSET Math: Plane Euclidean Geometry - Chapter Summary
Use the lessons in this chapter to help you understand similarity and congruence. You'll also learn how to apply properties of polygons, circles and triangles. Instructors provide examples and practice problems so you can learn to use these tactics in preparation for the exam. Videos cover the methods below, which are similar to questions on the exam:
- Determining properties of congruent and similar shapes
- Proving the angle-angle-side theorem
- Proving the hypotenuse angle and hypotenuse leg theorem
- Applying the law of sines and law of cosines
- Using the Pythagorean Theorem
- Determining the formula for area of polygons and circles
- Applying the angle bisector and perpendicular bisector theorems
- Creating perpendicular bisectors and N-Gons
- Proving geometric theorems with coordinate geometry
CSET Math: Plane Euclidean Geometry Objectives
Aspiring math teachers in California need to take the CSET Math exam to become certified. This exam tests your comprehension of critical math concepts, including those in geometry. Three subtests make up the exam, and you'll find questions on Plane Euclidean Geometry in Subtest II, which has 30 multiple choice questions and four constructed response questions.
To get used to the style of questions on the exam before taking it, use the self-assessment quizzes that accompany each lesson. These quizzes are also helpful for gauging your understanding of the subject matter as you prepare for the exam.
1. Similar Polygons: Definition and Examples
Watch this video to learn what makes two polygons similar to each other. You'll also learn the one distinguishing aspect of similar polygons and see an example of how to compare two polygons.
2. 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.
3. 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.
4. Triangle Congruence Postulates: SAS, ASA & SSS
When we have two triangles, how can we tell if they're congruent? They may look the same, but you can be certain by using one of several triangle congruence postulates, such as SSS, SAS or ASA.
5. Congruence Proofs: Corresponding Parts of Congruent Triangles
Congruent triangles have congruent sides and angles, and the sides and angles of one triangle correspond to their twins in the other. In this lesson, we'll try practice with some geometric proofs based around this theorem.
6. The AAS (Angle-Angle-Side) Theorem: Proof and Examples
When trying to find out if triangles are congruent, it's helpful to have as many tools as possible. In this lesson, we'll add to our congruence toolbox by learning about the AAS theorem, or angle-angle-side.
7. The HA (Hypotenuse Angle) Theorem: Proof, Explanation, & Examples
In this lesson, we'll learn about the hypotenuse angle theorem. With this theorem, we can prove two right triangles are congruent with just congruent hypotenuses and acute angles.
8. The HL (Hypotenuse Leg) Theorem: Definition, Proof, & Examples
In this lesson, we'll learn about the hypotenuse leg theorem. This theorem enables us to prove two right triangles are congruent based on just two sides.
9. Interior and Exterior Angles of Triangles: Definition & Examples
Knowing just a few things about the interior or exterior angles of triangles is sometimes all you need to put all the pieces together. Find out more in this lesson.
10. Law of Sines: Definition and Application
Don't get stuck trying to find missing sides or angles in a triangle. Use the Law of Sines to rescue you from any perilous triangle in which you have just a few pieces of information.
11. Law of Cosines: Definition and Application
In this lesson, we'll learn how to solve problems involving three sides and one angle in a triangle. The Law of Cosines, a modification of the Pythagorean Theorem, will save the day.
12. 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.
13. The Pythagorean Theorem: Converse and Special Cases
The Pythagorean Theorem is a famous theorem for right triangles. Watch this video to learn how the Pythagorean Theorem relates to the law of cosines and how the converse of the Pythagorean Theorem can help you identify right triangles.
14. Angle Bisector Theorem: Proof and Example
The angle bisector theorem sounds almost too good to be true. In this lesson, we set out to prove the theorem and then look at a few examples of how it's used.
15. 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.
16. Perpendicular Bisector Theorem: Proof and Example
Perpendicular bisectors are multifunctional lines. They're not only perpendicular to the line in question, they also neatly divide it into two equal halves. In this lesson, we'll learn about the perpendicular bisector theorem.
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