About This Chapter
High School Geometry: Quadrilaterals - Chapter Summary and Learning Objectives
Think geometry's for the birds? Not exactly. In this chapter, the kites and herons actually refer to a familiar quadrilateral and a Greek mathematician. Within this group of lessons, you can explore a variety of four-sided shapes. In addition to a kite, you can also learn to work with a rhombus, rectangle, trapezoid, square and parallelogram. You can also meet Heron and find out how to use his geometric formula. This chapter is designed to teach you:
- Properties of parallelograms, rhombi, kites, rectangles, squares and trapezoids
- Various theorems, constructions and calculations with quadrilaterals
- Division of line segments into equal parts
- Uses for Heron's geometric formula
|Parallelograms: Definition, Properties, and Proof Theorems||Define and illustrate a parallelogram. State the properties of a parallelogram and theorems to prove a quadrilateral is a parallelogram.|
|Measuring the Area of a Parallelogram||Explain how to measure the area of a parallelogram.|
|What Is a Rhombus? - Definition and Properties||Define and illustrate a rhombus. Explain why a quadrilateral is a rhombus. Discuss properties of a rhombus.|
|Measuring the Area of a Rhombus||Explain the formula for measuring the area of a rhombus.|
|Kites in Geometry: Definition and Properties||Define and illustrate a kite. Discuss the properties of a kite, including those it shares with the rhombus.|
|Rectangles: Definition, Properties & Construction||Define and illustrate a rectangle. Discuss the properties of rectangles. Discuss the construction of a rectangle.|
|Measuring the Area of a Rectangle||Explain how to apply the area of a rectangle formula.|
|Squares: Definition and Properties||Explain the characteristics of a square and illustrate one. Discuss the properties of a square.|
|Trapezoids: Definition and Properties||Define and illustrate a trapezoid and an isosceles trapezoid. Discuss properties of trapezoids.|
|Measuring the Area of a Trapezoid||Explain the formula used for measuring the area of a trapezoid. Describe the variables used in the formula.|
|Dividing Line Segments into Equal Parts||Describe how to divide a given line segment into any number of equal parts.|
|Using Heron's Formula in Geometry||Describe Heron's contributions to geometry. Explain how to use Heron's formula.|
1. Parallelograms: Definition, Properties, and Proof Theorems
Watch this video lesson to learn how you can identify parallelograms. You will see the unique properties that belong to the parallelogram. You will see the special side and angle characteristics needed to prove a certain shape is a parallelogram.
2. Measuring the Area of a Parallelogram: Formula & Examples
Watch this video lesson to learn the simple formula to find the area of a parallelogram. Learn what measurements you need, how to label your parallelogram, and how to use the formula.
3. What Is a Rhombus? - Definition and Properties
Watch this video lesson to learn why rhombuses are a special type of quadrilateral. Also, learn why a rhombus is also a parallelogram. Watch as we explore the sides and angles of a rhombus.
4. Measuring the Area of a Rhombus: Formula & Examples
Did you know that there are three ways to find the area of a rhombus? Watch this video lesson to learn all three of them. See what information you need for each method as well as the steps required for each.
5. Kites in Geometry: Definition and Properties
A kite in geometry looks a lot like a kite in the sky! Watch this video lesson to see for yourself. Also, learn about the side and angle properties of kites that make them unique.
6. Rectangles: Definition, Properties & Construction
Watch this video lesson to learn a bit about rectangles. Learn why rectangles are the building blocks of many homes. Also, learn about the properties that make a rectangle unique from other shapes. Finally, learn how you can draw one.
7. Measuring the Area of a Rectangle: Formula & Examples
Look around you, and you see rectangles all over the place. And if you see paint, carpet, or anything that covers a rectangular area, you can be sure that someone has measured the area of the rectangle. Watch this video lesson to learn more.
8. Squares: Definition and Properties
Squares can be found in many places in the real world. Watch this video lesson to see how useful they can be and also to learn how to find the perimeter and area of a square.
9. Trapezoids: Definition and Properties
Watch this video lesson to learn what a trapezoid has to do with a triangle. Also, learn the special words that describe the various parts of a trapezoid. You will also see special types of trapezoids.
10. Measuring the Area of a Trapezoid
In this video lesson, you will watch and learn how you can find the area of trapezoid. Learn what measurements you need to have on hand as well as the formula that you need to use.
11. Using Heron's Formula in Geometry
Heron's formula has been around for a couple thousand years. Watch this video lesson to see how you can use Heron's formula to find the area of a triangle while only knowing the side lengths.
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Other chapters within the Geometry: High School course
- High School Geometry: Foundations of Geometry
- High School Geometry: Logic in Mathematics
- High School Geometry: Introduction to Geometric Figures
- High School Geometry: Properties of Triangles
- High School Geometry: Triangles, Theorems and Proofs
- High School Geometry: Parallel Lines and Polygons
- High School Geometry: Similar Polygons
- High School Geometry: Circular Arcs and Circles
- High School Geometry: Conic Sections
- High School Geometry: Geometric Solids
- High School Geometry: Analytical Geometry
- High School Geometry: Probability
- High School Geometry: Introduction to Trigonometry