# Ch 4: Properties of Triangles: Tutoring Solution

### About This Chapter

## How it works:

- Begin your assignment or other high school geometry work.
- Identify the properties of triangles concepts that you're stuck on.
- Find fun videos on the topics you need to understand.
- Press play, watch and learn!
- Complete the quizzes to test your understanding.
- As needed, submit a question to one of our instructors for personalized support.

## Who's it for?

This chapter of our high school geometry tutoring solution will benefit any student who is trying to learn about the properties of triangles and earn better grades. This resource can help students including those who:

- Struggle with understanding classification of triangles, identification of similar triangles, construction of a triangle's median or any other properties of triangles topic
- Have limited time for studying
- Want a cost effective way to supplement their math learning
- Prefer learning math visually
- Find themselves failing or close to failing their properties of triangles unit
- Cope with ADD or ADHD
- Want to get ahead in high school geometry
- Don't have access to their math teacher outside of class

## Why it works:

**Engaging Tutors:**We make learning about the properties of triangles simple and fun.**Cost Efficient:**For less than 20% of the cost of a private tutor, you'll have unlimited access 24/7.**Consistent High Quality:**Unlike a live algebra tutor, these video lessons are thoroughly reviewed.**Convenient:**Imagine a tutor as portable as your laptop, tablet or smartphone. Learn about the properties of triangles on the go!**Learn at Your Pace:**You can pause and rewatch lessons as often as you'd like, until you master the material.

## Learning objectives

- Define and assess the parts of a triangle.
- Find the area and perimeter of rectangles and triangles.
- Learn about the main kinds of triangles and classify them by their angles.
- Identify similar triangles as well as the interior and exterior angles of triangles.
- Practice solving angles and triangles.
- Construct a congruent triangle as well as the median of a triangle.
- Identify the altitude, median and angle bisectors of a triangle.
- Learn about a triangle's properties of concurrent lines and the properties of dilations.

### 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.

### 12. 30-60-90 Triangle: Theorem, Properties & Formula

This lesson will explore a specific kind of right triangle, the 30-60-90 right triangle, including the relationships that exist between the sides and angles in them.

### 13. 45-45-90 Triangle: Theorem, Rules & Formula

This lesson will teach you about one of the special right triangles, the 45-45-90 triangle. You will learn the formulas for calculating the lengths of the sides of this type of triangle. After the lesson, you will be able to test your knowledge with a quiz.

### 14. Complementary Angles: Definition, Theorem & Examples

In this lesson, we will define complementary angles and see how they may appear in diagrams. We will discuss two common theorems that involve complementary angles. Then you can test your knowledge with a quiz.

### 15. Consecutive Interior Angles: Definition & Theorem

In this lesson, you will learn what a transversal has to do with consecutive interior angles as well as learning how the theorem ties in with parallel lines. Finally, you will see the information in action.

### 16. Exterior Angle Theorem: Definition & Formula

While it may sound scary at first, the exterior angle theorem is a simple formula that helps us solve for the missing angle of a triangle. Rather than examining a formal proof of the theorem, we'll focus on the formula itself and how it can be applied.

### 17. Half Angle: Rule, Formula & Examples

If we know at least the cosine of an angle, we can use formulas to find the sine, cosine and tangent of half that angle. These formulas are called half-angle formulas. In this lesson we state half-angle formulas, describe the rules for using them, and present examples.

### 18. Perfect Parabola: Definition & Explanation

Perfect parabolas are created from formulas and can also be hand-drawn. Learn how you can draw your own and what the mathematical formulas look like. Also learn what makes a parabola perfect.

### 19. Same-Side Exterior Angles: Definition & Theorem

Many kinds of angles are formed by intersecting lines. In this lesson, you'll learn the definition and theorem of same-side exterior angles. Then, take a brief quiz to check what you learned.

### 20. Same-Side Interior Angles: Definition & Theorem

In this lesson, you will learn the definition of same-side interior angles, their properties when they lie on parallel lines, and the same-side interior angle theorem. At the end, you can test your knowledge with a quiz.

### 21. How to Find the Centroid of a Triangle

The centroid of a triangle is its center-most point. This point is an equal distance from each corner (vertex) of the triangle. To find the centroid you find the average of the x and y values of the vertices.

### 22. How to Find Amplitude of a Sine Function

In this lesson we look at a method for finding the amplitude of a sine function. This method works even when the equilibrium line is not the horizontal axis.

### 23. How to Find the Area of an Equilateral Triangle

Learn how you can easily find the area of an equilateral triangle. Find out what number you need to be given before you start to solve it as well as the formula to use to plug in that number.

### 24. How to Find the Area of an Isosceles Triangle

In this lesson, we'll learn how to find the area of an isosceles triangle. We'll also look at how to find the height of an isosceles triangle given the lengths of its sides, since this is needed to find the area.

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### Other Chapters

Other chapters within the High School Geometry: Tutoring Solution course

- Foundations of Geometry: Tutoring Solution
- Logic in Mathematics: Tutoring Solution
- Introduction to Geometric Figures: Tutoring Solution
- Triangles, Theorems and Proofs: Tutoring Solution
- Parallel Lines and Polygons: Tutoring Solution
- Similar Polygons: Tutoring Solution
- Quadrilaterals: Tutoring Solution
- Symmetry, Similarity and Congruence
- Circular Arcs and Circles: Tutoring Solution
- Conic Sections: Tutoring Solution
- Geometric Solids: Tutoring Solution
- Analytical Geometry: Tutoring Solution
- Introduction to Trigonometry: Tutoring Solution