# Ch 8: NY Regents - Triangles and Congruency: Tutoring Solution

### About This Chapter

## How it works:

- Begin your assignment or other geometry work.
- Identify the triangles and congruency concepts that you're stuck on.
- Find fun videos on the topics you need to understand for the NY Regents Exam.
- 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 NY Regents Geometry Exam Tutoring Solution will benefit any student who is trying to learn about triangles and congruency for the NY Regents Exam and earn passing scores. This resource can help students including those who:

- Struggle with understanding angles, bisectors, proofs or any other triangles and congruency topic
- Have limited time for studying
- Want a cost effective way to supplement their math learning for the NY Regents Exam
- Prefer learning about math visually
- Find themselves failing or close to failing their triangles and congruency unit
- Cope with ADD or ADHD
- Want to get ahead in geometry
- Don't have access to their math teacher outside of class

## Why it works:

**Engaging Tutors:**We make learning about triangles and congruency 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 geometry tutor, these video lessons are thoroughly reviewed.**Convenient:**Imagine a tutor as portable as your laptop, tablet or smartphone. Learn about triangles and congruency for the NY Regents Exam 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

- List the properties of triangles.
- Be able to find the areas of triangles and rectangles.
- Learn how to classify triangles by their angles and sides.
- Determine the perimeters of triangles and rectangles.
- Take a look at examples of interior and exterior angles of triangles.
- Identify similar triangles.
- Become familiar with the triangle congruence postulates.
- Understand the applications of similar triangles.
- Learn how to construct congruence proofs.
- Discuss the perpendicular bisector theorem and angle bisector theorem.
- Prove the congruency of isosceles triangles.
- Provide examples of the converse of a statement.
- Be able to find the altitude, median and bisectors of a triangle.
- List the properties of concurrent lines in a triangle.
- Define the LA and LL theorems that help prove the congruency of right triangles.
- Become familiar with the different types of geometric construction.
- Construct a triangle's median.
- Learn about the AAS theorem.
- Discuss the HA and HL theorems.
- Understand the properties of dilations.
- Perform similarity transformations.
- Use congruence and similarity in order to prove relationships in figures.

### 1. 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.

### 2. 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.

### 3. 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.

### 4. 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.

### 5. 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.

### 6. 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.

### 7. 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.

### 8. Applications of Similar Triangles

Similar triangles are used to solve problems in everyday situations. Learn how to solve with similar triangles here, and then test your understanding with a quiz.

### 9. 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.

### 10. Perpendicular Bisector Theorem: Proof and Example

Perpendicular bisectors are multifunctional lines. They're not only perpendicular to the line in question, they also neatly divide it into two equal halves. In this lesson, we'll learn about the perpendicular bisector theorem.

### 11. Angle Bisector Theorem: Proof and Example

The angle bisector theorem sounds almost too good to be true. In this lesson, we set out to prove the theorem and then look at a few examples of how it's used.

### 12. Congruency of Isosceles Triangles: Proving the Theorem

Isosceles triangles have two equal sides. Are the base angles also equal? In this lesson, we'll prove how this is true. We'll also prove the theorem's converse.

### 13. Converse of a Statement: Explanation and Example

Just because a conditional statement is true, is the converse of the statement always going to be true? In this lesson, we'll learn the truth about the converse of statements.

### 14. 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.

### 15. 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.

### 16. 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.

### 17. Congruency of Right Triangles: Definition of LA and LL Theorems

In this lesson, we'll learn two theorems that help us prove when two right triangles are congruent to one another. The LA theorem, or leg-acute, and LL theorem, or leg-leg, are useful shortcuts for proving congruence.

### 18. 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.

### 19. 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.

### 20. 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.

### 21. 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.

### 22. 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.

### 23. Congruent Sides of a Triangle: Definition & Overview

This lesson will teach you the concept of congruency as applied to the sides of a triangle. It will also teach you how the classification of a triangle by its sides is dependent on its number of congruent sides.

### 24. Dihedral Angle: Definition & Calculation

Dihedral angles show up frequently in the world around us. Through definition and example, we will learn what a dihedral angle is and how to calculate it. After you finish the lesson, you can test your new-found knowledge with a quiz!

### 25. Double Angle: Properties, Rules, Formula & Examples

Understanding the double angle formula is important to trigonometry. This lesson will help you to see the connections between the trigonometric ratios as they relate to the double angle formula.

### 26. Percent Increase: Definition & Formula

This lesson will examine how to find the percent increase between two values. It will look at finding the percent increase between both numbers and percentages.

### 27. Sine: Definition & Examples

Sine is one of the three main trigonometric ratios. It's based on the measurements of a right triangle and helps you find angle measures and distances, among other things. This lesson defines the sine function and gives examples of when it is used.

### 28. Slope-Intercept Form: Definition & Examples

The slope-intercept form of the equation of a line is a useful form for graphing as well as for understanding the relationship between x and y. In this lesson, learn how the slope-intercept form helps you understand the equation of a line.

### 29. Vertical Angles in Geometry: Definition & Examples

After completing this lesson, you will be able to identify and draw vertical angles. You will also be able to state the properties of vertical angles. After the lesson, test yourself with a quiz.

### 30. What Are Adjacent Angles? - Definition & Examples

In this lesson, you will learn how to identify whether angles are adjacent. After looking at several examples, you will be able to test your knowledge with a quiz.

### 31. What is a Central Angle? - Definition, Theorem & Formula

In this lesson, you will learn about the definition and properties of a central angle. You will also discover what the Central Angle Theorem is and what the formula is for central angles. Test your new knowledge with a quiz.

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### Other Chapters

Other chapters within the NY Regents Exam - Geometry: Tutoring Solution course

- NY Regents - Foundations of Geometry: Tutoring Solution
- NY Regents - Logic in Mathematics: Tutoring Solution
- NY Regents - Introduction to Geometric Figures: Tutoring Solution
- NY Regents - Similar Polygons: Tutoring Solution
- NY Regents - Quadrilaterals: Tutoring Solution
- NY Regents - Circular Arcs and Circles: Tutoring Solution
- NY Regents - Analytical Geometry: Tutoring Solution
- NY Regents - Parallel Lines and Polygons: Tutoring Solution
- NY Regents - Geometric Solids: Tutoring Solution