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Ch 32: Praxis Mathematics: Congruence, Similarity and Transformations

About This Chapter

Let us teach you about congruence and similarity. The video lessons and self-assessment quizzes in this chapter can prepare you to answer questions about geometry on the Praxis Mathematics: Content Knowledge test.

Praxis Mathematics: Content Knowledge - Congruence and Similarity: Chapter Summary

Prospective high school mathematics teachers who need a refresher on congruence and similarity before taking the Praxis Mathematics: Content Knowledge test can utilize this chapter. Featured video lessons will teach you about congruence and corresponding pairs of sides or angles. You'll also learn how to determine whether triangles are congruent using the ASA (angle side angle), SAS (side angle side) and SSS (side side side) methods. Other topics of study include proving similarity theorems about triangles and recognizing similarity in circles.

Praxis Mathematics: Content Knowledge - Congruence and Similarity Objectives

A number of states use the Praxis Mathematics: Content Knowledge test in their certification process for high school mathematics teachers. This test is offered in a computer-based format in various 12-day windows throughout the year and in a paper-based format four times a year. Test-takers have two hours to complete 50 multiple-choice questions, some of which require a graphing calculator. Questions about congruence and similarity might be included in the geometry content category, which makes up approximately ten percent of this Praxis test.

Our chapter on congruence and similarity is taught by experienced professional math instructors. Each lesson in this chapter includes a video presentation and a corresponding self-assessment quiz. The quiz is designed to familiarize you with the types of questions you might encounter in the geometry section of the Praxis.

7 Lessons in Chapter 32: Praxis Mathematics: Congruence, Similarity and Transformations
Test your knowledge with a 30-question chapter practice test
Properties of Congruent and Similar Shapes

1. 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.

Congruence Proofs: Corresponding Parts of Congruent Triangles

2. 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.

Triangle Congruence Postulates: SAS, ASA & SSS

3. 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.

The HL (Hypotenuse Leg) Theorem: Definition, Proof, & Examples

4. 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.

The HA (Hypotenuse Angle) Theorem: Proof, Explanation, & Examples

5. 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.

The AAS (Angle-Angle-Side) Theorem: Proof and Examples

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.

Constructing Similar Polygons

7. Constructing Similar Polygons

This lesson will teach you how to construct similar polygons, which are very useful in many quantitative fields. You'll learn that all of this has something to do with, of all things, snowflakes!

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

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Other Chapters

Other chapters within the Praxis Mathematics - Content Knowledge (5161): Practice & Study Guide course

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