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 55,000 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

- FTCE ESOL K-12 (047): Practice & Study Guide
- GACE Media Specialist Test II: Practice & Study Guide
- GACE Media Specialist Test I: Practice & Study Guide
- GACE Political Science Test II: Practice & Study Guide
- NES Essential Components of Elementary Reading Instruction: Test Practice & Study Guide
- 20th Century Spanish Literature
- Sun, Moon & Stars Lesson Plans
- Direct Action & Desegregation from 1960-1963
- Civil Rights Movement from the Civil War to the 1920s
- Civil Rights in the New Deal & World War II Era
- Common Core State Standards in Ohio
- Resources for Assessing Export Risks
- Preview Personal Finance
- California School Emergency Planning & Safety Resources
- Popsicle Stick Bridge Lesson Plan
- California Code of Regulations for Schools
- WV Next Generation Standards for Math

- The Chorus in Antigone
- Where is Mount Everest Located? - Lesson for Kids
- Sperm Cell Facts: Lesson for Kids
- The Motivational Cycle: Definition, Stages & Examples
- Bolivian President Evo Morales: Biography & Quotes
- Labor Unions for Physicians: Benefits & Factors
- Positive Attitude & Call Center Performance
- Chicken Facts: Lesson for Kids
- Quiz & Worksheet - Converting English Measurement Units
- Quiz & Worksheet - What Is Felony Murder?
- Quiz & Worksheet - Characteristics of Agile Companies
- Quiz & Worksheet - A Bend in the River
- Quiz & Worksheet - Sentence Fluency
- Growth & Opportunity for Entrepreneurs Flashcards
- Understanding Customers as a New Business Flashcards

- CEOE Business Education: Practice & Study Guide
- Microsoft Excel Certification: Practice & Study Guide
- AP Physics 1: Homeschool Curriculum
- ORELA Middle Grades Social Science: Practice & Study Guide
- Smarter Balanced Assessments - Math Grade 8: Test Prep & Practice
- Introduction to Programming: Tutoring Solution
- Fitness for Personal Health
- Quiz & Worksheet - Patient Education for Adults
- Quiz & Worksheet - AP Psychology Exam Overview
- Quiz & Worksheet - Applying Scale Factors to Similar Figures
- Quiz & Worksheet - Characteristics of ADD & Other Disruptive Behavior Disorders
- Quiz & Worksheet - Finding Constant and Average Rates

- The Theory of Attribution In Organizational Behavior: Definition and Three Determinants
- Transcription Factor: Definition & Identification
- Free Online GED Classes
- Harlem Renaissance Lesson Plan
- What Is the SAT Subject Test?
- Parallel & Perpendicular Lines Lesson Plan
- GED Test Registration Dates
- Subject-Verb Agreement Lesson Plan
- Free GED Classes
- What is the New SAT?
- The New SAT vs. the Old SAT
- And Then There Were None Lesson Plan

Browse by subject