About This Chapter
Who's it for?
Anyone who needs help learning or mastering geometry material for the NY Regents Exam will benefit from taking this course. There is no faster or easier way to learn high school geometry. Among those who would benefit are:
- Students who have fallen behind in understanding the definition and properties of triangles and their proofs and theorems
- Students who struggle with learning disabilities or learning differences, including autism and ADHD
- Students who prefer multiple ways of learning math (visual or auditory)
- Students who have missed class time and need to catch up
- Students who need an efficient way to learn about triangles and congruency for the NY Regents Exam
- Students who struggle to understand their teachers
- Students who attend schools without extra math learning resources
How it works:
- Find videos in our course that cover what you need to learn or review.
- Press play and watch the video lesson.
- Refer to the video transcripts to reinforce your learning.
- Test your understanding of each lesson with short quizzes.
- Verify you're ready by completing the Triangles and Congruency chapter exam.
Why it works:
- Study Efficiently: Skip what you know, review what you don't.
- Retain What You Learn: Engaging animations and real-life examples make topics easy to grasp.
- Be Ready on Test Day: Use the Triangles and Congruency chapter exam to be prepared.
- Get Extra Support: Ask our subject-matter experts any triangles and congruency question. They're here to help!
- Study With Flexibility: Watch videos on any web-ready device.
Students will review:
This chapter helps students review the concepts in a triangles and congruency unit of a standard high school geometry course. Topics covered include:
- Definition and properties of triangles
- Classification of triangles
- Perimeter of triangles and rectangles
- Interior and exterior angles of triangles
- Triangle congruence postulates
- Congruence proofs
- Perpendicular bisector theorem
- Angle bisector theorem
- Congruency of isosceles triangles
- Median, altitude and angle bisectors of a triangle
- Properties of concurrent lines in a triangle
- Congruency of right triangles
- Construction of triangles and the median of triangles
- Properties of dilations
- Similarity transformations
- Proofs of relationships in figures using congruence and similarity
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. AA Similarity Postulate & Theorem
The AA similarity postulate and theorem can be useful when dealing with similar triangles. In this lesson, we will examine this postulate, see how and why it works, and put it to use in various examples.
24. Circumcenter: Definition, Formula & Construction
This lesson will examine the circumcenter of a triangle. We will discuss the definition, location and demonstrate how to construct and identify the circumcenter.
25. Half-Angle: Formulas & Proof
Half-angle formulas extend our vocabulary of the common trig functions. After reviewing some fundamental math ideas, this lesson uses theorems to develop half-angle formulas for sine, cosine and tangent.
26. Intercepted Arc: Definition & Formula
Very often, as we look around our world, we see parts of circles. In this lesson, we will take a look at the arc that runs along the circumference of the circle in between the two chords, called the intercepted arc.
27. Percent Decrease: Formula & Calculation
Many values we come across on a regular basis change frequently. In this lesson we will look at examples when a quantity decreases in value, and how such decreases can be represented using percentages.
28. Similar Triangles: Definition, Formula & Properties
Similar triangles are triangles with equal corresponding angles and proportionate sides. This lesson will explore the proprieties of similar triangles and explain how to apply these properties to solve for the length of missing sides.
29. Slope Triangle: Definition & Concept
In this lesson, you will learn about slope triangles, a kind of triangle that helps you easily find the slope of a line or line segment. Often, these are imaginary triangles sketched between two points.
30. Trigonal Planar in Geometry: Structure, Shape & Examples
In this lesson you will learn about the shape and structure of trigonal planar molecules. We will discuss the angles formed within the molecules and look at a few examples. You can then take a brief quiz to see what you learned.
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Other chapters within the NY Regents Exam - Geometry: Help and Review course
- NY Regents - Foundations of Geometry: Help and Review
- NY Regents - Logic in Mathematics: Help and Review
- NY Regents - Introduction to Geometric Figures: Help and Review
- NY Regents - Similar Polygons: Help and Review
- NY Regents - Quadrilaterals: Help and Review
- NY Regents - Circular Arcs and Circles: Help and Review
- NY Regents - Analytical Geometry: Help and Review
- NY Regents - Parallel Lines and Polygons: Help and Review
- NY Regents - Geometric Solids: Help and Review
- NY Regents Exam - Geometry Help and Review Flashcards