# Ch 4: High School Geometry: Properties of Triangles

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### About This Chapter

## High School Geometry: Properties of Triangles - Chapter Summary and Learning Objectives

You can learn the formulas to find the area and perimeter of triangles and rectangles in these lessons, and then work your way through the practice problems for additional support. Discover how to classify triangles by their sides and angles, in addition to learning ways to identify similar triangles. When you finish this chapter, you should be able to:

- Construct triangles
- Understand the properties of dilations
- Construct the median of a triangle
- Find the median, altitude and angle bisectors of triangles

Video | Objectives |
---|---|

Triangles: Definition and Properties | Define and illustrate a triangle. Identify the parts of a triangle. |

Area of Triangles and Rectangles | Learn to find the area of triangles and rectangles and apply that knowledge to find the areas of other related shapes. |

Classifying Triangles by Angles and Sides | Explain how to classify triangles by their sides and angles. Describe common types of triangles. |

Perimeter of Triangles and Rectangles | Learn perimeter of triangles and rectangles and apply to solve various problems. |

Interior and Exterior Angles of Triangles | Define and identify the interior and exterior angles of a triangle, providing examples. |

How to Identify Similar Triangles | Learn how to identify similar triangles through an understanding of corresponding, proportional and included angle parts. |

Angles and Triangles: Practice Problems | Gain practice solving for angles and triangles. |

Constructing the Median of a Triangle | Describe how to construct the median of a triangle, providing examples. |

Median, Altitude, and Angle Bisectors of a Triangle | Define median, altitude and angle bisectors of a triangle. Demonstrate how to identify those in an example. |

Constructing Triangles | Explain how to construct a triangle that is congruent to a given triangle. Demonstrate how to construct a triangle with two sides and the included angle. |

Properties of Concurrent Lines in a Triangle | Discuss properties, including centroid, altitude, angle bisector, incenter and orthocenter. |

Properties of Dilations | Understand that a dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. |

### 1. 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.

### 2. 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.

### 3. 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.

### 4. 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.

### 5. Triangles: Definition and Properties

What makes a shape a triangle? In this lesson, we'll explore the definition of a triangle, then analyze the parts of triangles, including the vertices, base and height.

### 6. Classifying Triangles by Angles and Sides

Not all triangles are the same. There are equilateral, isosceles and scalene triangles. Then there are right, acute and obtuse triangles. In this lesson, we'll learn how to classify triangles using their sides and angles.

### 7. 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.

### 8. Constructing the Median of a Triangle

If you have one triangle and want to divide it, you can use a median line. Medians have special geometric properties that we'll learn about in this lesson.

### 9. Median, Altitude, and Angle Bisectors of a Triangle

Line segments in triangles are just clutter; they have special names and qualities depending on how they're drawn. In this lesson, we'll learn about medians, altitudes and angle bisectors.

### 10. Constructing Triangles: Types of Geometric Construction

When you're asked to construct a triangle, it's time to break out that compass and straight edge! In this lesson, find out how to construct triangles no matter what you're given.

### 11. Properties of Concurrent Lines in a Triangle

Centroids, orthocenters, incenters, circumcenters, oh my! Don't worry though. In this lesson, we master the various terms for concurrent lines in triangles and match them to altitudes, angle bisectors, perpendicular bisectors and medians.

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### Other Chapters

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: Triangles, Theorems and Proofs
- High School Geometry: Parallel Lines and Polygons
- High School Geometry: Similar Polygons
- High School Geometry: Quadrilaterals
- 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
- Teacher Resources for High School Geometry