Back To Course

NY Regents Exam - Geometry: Help and Review10 chapters | 127 lessons

Watch short & fun videos
**
Start Your Free Trial Today
**

Start Your Free Trial To Continue Watching

As a member, you'll also get unlimited access to over 70,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Free 5-day trial
Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Kimberlee Davison*

Kim has a Ph.D. in Education and has taught math courses at four colleges, in addition to teaching math to K-12 students in a variety of settings.

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.

A **slope triangle** is a visual tool that helps you find the slope of a line. By '**slope**,' we mean steepness.

Imagine that you are flying a plane and have ascended (vertically) 1,000 feet. When you are 1,000 feet above the ground, you have traveled forward (horizontally) 3,000 feet. With those two measurements, you can figure out how steep your ascent was. The higher the plane rises while it travels forward a certain amount, the steeper the incline.

If you look at the picture of the airplane's ascent, you'll see a triangle. This triangle is imaginary, of course. It is a visual tool, a 'slope triangle,' that helps you calculate how steep the ascent was. In other words, it helps you figure out the slope of the line connecting the plane's starting point to its current position.

One formula for slope you may have seen looks like this:

*Slope = rise/run*

The rise is the vertical distance on the triangle. The run is the horizontal distance. For our airplane, we get:

Slope = 1,000 feet/3,000 feet = 1/3

In other words, the airplane rises 1 foot vertically every time it travels 3 feet along the ground.

If a plane is 2,000 feet above the ground after it has traveled 3,000 feet forward, then its ascent is steeper. For the same horizontal distance traveled, it has reached a greater height. In this case, the slope triangle is less flat. The horizontal leg of the triangle is longer.

Slope = rise/run = 2,000 ft/3,000 ft = 2/3

The slope of the first airplane's ascent, 1/3, is less than the slope of the second airplane, 2/3. The second airplane travels upward more steeply.

Sometimes you may want to find the slope of a line, a line segment, or an imaginary line segment between two points. In the picture, the red dot is at the point (1,2). The blue dot is at the point (2,4). You can draw in a slope triangle by connecting the two points and creating the horizontal and vertical legs of a triangle.

The rise is the length of the vertical leg, 2 units. The run is the length of the horizontal leg, 1 unit. The slope is found by dividing:

Slope = rise/run = 2/1 = 2

Slope triangles work when a line slants downward as well. In the next picture, the blue dot (2,4) is higher than the red dot (5,2). In this case, the rise is -2 because you are moving downward from left to right. So, rise/run = -2/3. If the dots represented an airplane's location, then the airplane would be descending, or moving closer to the earth.

A **slope triangle** is an imaginary triangle that helps you find the slope of a line or a line segment. The hypotenuse of the triangle (the diagonal) is the line you are interested in finding the slope of. The two 'legs' of the triangle are the 'rise' and 'run' used in the slope formula. *Slope = rise/run*.

To unlock this lesson you must be a Study.com Member.

Create
your account

Already a member? Log In

BackDid you know… We have over 95 college courses that prepare you to earn credit by exam that is accepted by over 2,000 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
29 in chapter 8 of the course:

Back To Course

NY Regents Exam - Geometry: Help and Review10 chapters | 127 lessons

- Triangles: Definition and Properties 4:30
- Area of Triangles and Rectangles 5:43
- Classifying Triangles by Angles and Sides 5:44
- Perimeter of Triangles and Rectangles 8:54
- Interior and Exterior Angles of Triangles: Definition & Examples 5:25
- How to Identify Similar Triangles 7:23
- Triangle Congruence Postulates: SAS, ASA & SSS 6:15
- Applications of Similar Triangles 6:23
- Congruence Proofs: Corresponding Parts of Congruent Triangles 5:19
- Perpendicular Bisector Theorem: Proof and Example 6:41
- Angle Bisector Theorem: Proof and Example 6:12
- Congruency of Isosceles Triangles: Proving the Theorem 4:51
- Converse of a Statement: Explanation and Example 5:09
- Median, Altitude, and Angle Bisectors of a Triangle 4:50
- Properties of Concurrent Lines in a Triangle 6:17
- Angles and Triangles: Practice Problems 7:43
- Congruency of Right Triangles: Definition of LA and LL Theorems 7:00
- Constructing Triangles: Types of Geometric Construction 5:59
- Constructing the Median of a Triangle 4:47
- The AAS (Angle-Angle-Side) Theorem: Proof and Examples 6:31
- The HA (Hypotenuse Angle) Theorem: Proof, Explanation, & Examples 5:50
- The HL (Hypotenuse Leg) Theorem: Definition, Proof, & Examples 6:19
- AA Similarity Postulate & Theorem 5:56
- Circumcenter: Definition, Formula & Construction
- Half-Angle: Formulas & Proof
- Intercepted Arc: Definition & Formula 2:47
- Percent Decrease: Formula & Calculation
- Similar Triangles: Definition, Formula & Properties 6:43
- Slope Triangle: Definition & Concept 3:14
- Go to NY Regents - Triangles and Congruency: Help and Review

- Finding & Retaining Talent in an Agile Organization
- Cultural Agility for Organizations
- Psychology 306: Advanced Abnormal Psychology
- Computer Science 108: Introduction to Networking
- Psychology 316: Advanced Social Psychology
- Agile Talent Retention Strategies
- Understanding Cultural Agility in Organizations
- Intro to Agile Organizations
- Barriers to Cultural Agility in the Workplace
- Finding Agile Workers
- Study.com CLEP Scholarship for Military Members
- Study.com Scholarship for Texas Students & Prospective Teachers
- Study.com Scholarship for Florida Students & Prospective Teachers
- What are TExMaT Exams?
- What is the Florida Teacher Certification Examination (FTCE)?
- Study.com TExES Scholarship: Application Form & Information
- Study.com FTCE Scholarship: Application Form & Information

- Challenges in Communicating With Customers Over the Phone
- Teaching Kids How to Count
- Managing Discounts & Plops in Team Meetings
- Forensic Serology: Definitions & Examples
- How to Manage Program-Level Issues
- Surah 55 in the Qur'an: Analysis & Symbolism
- Ethnic Groups in Africa
- What is the Negotiator's Dilemma?
- Quiz & Worksheet - Criminal Insanity Law
- Quiz & Worksheet - Vehicular Homicide & Law
- Quiz & Worksheet - Passive-Aggressiveness on the Job
- Quiz & Assessment - Tolstoy's God Sees the Truth But Waits
- Quiz & Worksheet - Preventing Burnout on Work Teams
- International Law & Global Issues Flashcards
- Foreign Policy, Defense Policy & Government Flashcards

- Calculus for Teachers: Professional Development
- Intro to Sociology Syllabus Resource & Lesson Plans
- US Citizenship Study Guide
- How to Prepare for a Job Interview
- Holt McDougal Larson Geometry: Online Textbook Help
- The Eastern Mediterranean
- Working With Inequalities: Homeschool Curriculum
- Quiz & Worksheet - Abiotic Synthesis of Organic Molecules
- Quiz & Worksheet - Moral Development Stages
- Quiz & Worksheet - Romanesque Architecture
- Quiz & Worksheet - Basic Psychological Processes
- Quiz & Worksheet - What is the Dolphin Food Chain?

- What Is Density? - Explanation & Examples
- Recombination: Definition & Process
- Found Poetry Lesson Plan
- Environmental Projects for Kids
- 2nd Grade Science Projects
- What Math is on the GRE?
- How to Sign Up for the ACT
- Average GRE Scores
- How to Pass the AP Biology Exam
- What are Passing Scores for GACE Tests?
- How to Study for the DSST
- 2nd Grade Writing Prompts

Browse by subject