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Ch 19: Illinois TAP Math: Geometry

About This Chapter

Let us help you master the principles of geometry as you prepare for the Illinois TAP Math exam. The video lessons and self-assessment quizzes will teach you definitions of geometric terms and basic calculations.

Illinois TAP Math: Geometry - Chapter Summary

The lessons from this chapter will make clear the geometry skills you'll need to pass the math portion of the Illinois TAP - Test of Academic Proficiency. In addition to learning about problems involving lines and angles, you'll study various two- and three-dimensional figures and learn to solve problems involving them, including calculating area, volume and perimeter. Topics covered in these lessons include:

  • Parallel, perpendicular and transverse lines
  • Vertical, corresponding, alternate interior and other types of angles
  • Properties of triangles, circles and rectangles
  • Properties of quadrilaterals, parallelograms, trapezoids and polygons
  • Properties of congruent and similar shapes
  • Perimeter of triangles and rectangles
  • Perimeter of quadrilaterals and irregular or combined shapes
  • Area of triangles, rectangles and complex figures
  • Area and circumference of circles
  • How to calculate the volumes of basic shapes
  • Volume of cylinders, cones and spheres
  • Volume of prisms and pyramids
  • Solving surface area problems

These engaging video lessons are led by expert instructors who will teach you the basics required to take on the TAP. As you explore methods of calculating surface area, perimeter and volume, you'll find that learning about these figures and their properties is enjoyable.

Objectives of the Illinois TAP Math: Geometry Course

All Illinois candidates for teacher licensing must pass the TAP, and the lessons in this chapter will help you correctly answer the exam's geometry questions. The TAP consists of 170 multiple-choice questions, divided into three subject areas, plus a writing test. The geometry questions are in the Mathematics portion, which contains 50 questions. By completing the self-assessment quizzes at the end of each video lesson, you'll get to check your preparation and become acquainted with the format of the test.

14 Lessons in Chapter 19: Illinois TAP Math: Geometry
Test your knowledge with a 30-question chapter practice test
Parallel, Perpendicular and Transverse Lines

1. 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.

Types of Angles: Vertical, Corresponding, Alternate Interior & Others

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.

Angles and Triangles: Practice Problems

3. 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.

Properties of Shapes: Rectangles, Squares and Rhombuses

4. 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.

Properties of Shapes: Quadrilaterals, Parallelograms, Trapezoids, Polygons

5. 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.

Properties of Congruent and Similar Shapes

6. 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.

Perimeter of Triangles and Rectangles

7. Perimeter of Triangles and Rectangles

Without realizing it, we calculate and use the perimeter of triangles and rectangles in regular everyday situations. Learn more about the perimeter of triangles and rectangles in this lesson, and test your knowledge with a quiz.

Perimeter of Quadrilaterals and Irregular or Combined Shapes

8. Perimeter of Quadrilaterals and Irregular or Combined Shapes

Sometimes you need to figure out a shape's perimeter whether you have all the information you want or not. In this lesson, you'll learn how to find the perimeter of any quadrilateral as well as more complicated irregular and combined shapes.

Area of Triangles and Rectangles

9. Area of Triangles and Rectangles

How do you find out the area of rectangles and triangles? Learn how in this lesson! We'll look at the formulas, then practice solving problems for each shape.

Area of Complex Figures

10. Area of Complex Figures

Finding the area of shapes isn't always as simple as it is with squares and rectangles. In this lesson, you'll learn how to find the area of complex figures. This includes finding the area of unusual shapes and finding the area of parts of shapes.

Circles: Area and Circumference

11. Circles: Area and Circumference

Understanding how to calculate the area and circumference of circles plays a vital role in some of our everyday functions. They serve as the foundation for operating with three-dimensional figures. Learn more about the area and circumference of circles in this lesson.

How to Calculate the Volumes of Basic Shapes

12. How to Calculate the Volumes of Basic Shapes

Squares pegs = square holes. Triangular pegs = triangular holes. But where does a sphere go? In this lesson, review volumes of common shapes while contrasting a sphere and a cylinder - after all, they both go into the circular hole... right?

Volume of Cylinders, Cones, and Spheres

13. Volume of Cylinders, Cones, and Spheres

In this lesson, we'll learn about the volume formulas for cylinders, cones and spheres. We'll also practice using the formula in a variety of real-world examples where knowing how to calculate volume is helpful.

Volume of Prisms and Pyramids

14. Volume of Prisms and Pyramids

In this lesson, we'll learn about prisms and pyramids. We'll look at the different types of prisms and pyramids, as well as practice calculating volume for each shape.

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

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