About This Chapter
ORELA Math: Properties of Triangles - Chapter Summary
These engaging, brief videos are designed to help educators master the triangle properties they're likely to be tested on as they work through the ORELA Math certification assessment. As you navigate the resources in this chapter, you'll review:
- Basic triangle properties and classifications
- Perimeter and area of triangles and rectangles
- Interior and exterior angles, median, altitude and angle bisectors
- Concurrent lines and dilations
- The Pythagorean theorem
Reach out to our instructors for guidance if you get stuck or confused. Make sure to take each of the multiple-choice lesson quizzes to test yourself on triangle properties and other information you've covered.
Objectives of the ORELA Math: Properties of Triangles Chapter
You'll need to know about triangle properties for the Measurement and Geometry portion of the ORELA Math certification assessment, which accounts for 19% of your score. Equally weighted are Math Processes and Number Sense; Trigonometry and Calculus; and Statistics, Probability and Discrete Mathematics. The final area of competency you will be tested on is Patterns, Algebra and Functions, which accounts for 24% of your score.
These short videos cover the triangle-related concepts you are expected to know for the Measurement and Geometry content area. You will have four hours and fifteen minutes to answer all 150 multiple-choice questions on the computer-based exam.
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. 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.
8. 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.
9. Properties of Right Triangles: Theorems & Proofs
In this lesson, you will learn about the properties of and theorems associated with right triangles, which have a wide range of applications in math and science. Specifically, we will discuss and prove the Pythagorean theorem and the right triangle altitude theorem. Let's get started.
10. The Pythagorean Theorem: Practice and Application
The Pythagorean theorem is one of the most famous geometric theorems. Written by the Greek mathematician Pythagoras, this theorem makes it possible to find a missing side length of a right triangle. Learn more about the famous theorem here and test your understanding with a quiz.
11. The Pythagorean Theorem: Converse and Special Cases
The Pythagorean Theorem is a famous theorem for right triangles. Watch this video to learn how the Pythagorean Theorem relates to the law of cosines and how the converse of the Pythagorean Theorem can help you identify right triangles.
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Other chapters within the ORELA Mathematics: Practice & Study Guide course
- ORELA Math: Properties of Real Numbers
- ORELA Math: Fractions
- ORELA Math: Decimals & Percents
- ORELA Math: Ratios & Proportions
- ORELA Math: Units of Measure & Conversions
- ORELA Math: Logic
- ORELA Math: Reasoning
- ORELA Math: Vector Operations
- ORELA Math: Matrix Operations & Determinants
- ORELA Math: Exponents & Exponential Expressions
- ORELA Math: Algebraic Expressions
- ORELA Math: Linear Equations
- ORELA Math: Inequalities
- ORELA Math: Absolute Value
- ORELA Math: Quadratic Equations
- ORELA Math: Polynomials
- ORELA Math: Rational Expressions
- ORELA Math: Radical Expressions
- ORELA Math: Systems of Equations
- ORELA Math: Complex Numbers
- ORELA Math: Functions
- ORELA Math: Piecewise Functions
- ORELA Math: Exponential & Logarithmic Functions
- ORELA Math: Continuity of a Function
- ORELA Math: Limits
- ORELA Math: Rate of Change
- ORELA Math: Calculating Derivatives & Derivative Rules
- ORELA Math: Graphing Derivatives
- ORELA Math: Applications of Derivatives
- ORELA Math: Area Under the Curve & Integrals
- ORELA Math: Integration Techniques
- ORELA Math: Applications of Integration
- ORELA Math: Foundations of Geometry
- ORELA Math: Geometric Figures
- ORELA Math: Triangle Theorems & Proofs
- ORELA Math: Parallel Lines & Polygons
- ORELA Math: Quadrilaterals
- ORELA Math: Circles & Arc of a Circle
- ORELA Math: Conic Sections
- ORELA Math: Geometric Solids
- ORELA Math: Analytical Geometry
- ORELA Math: Trigonometric Functions
- ORELA Math: Trigonometric Graphs
- ORELA Math: Solving Trigonometric Equations
- ORELA Math: Trigonometric Identities
- ORELA Math: Sequences & Series
- ORELA Math: Graph Theory
- ORELA Math: Set Theory
- ORELA Math: Statistics Overview
- ORELA Math: Summarizing Data
- ORELA Math: Tables, Plots & Graphs
- ORELA Math: Probability
- ORELA Math: Discrete Probability Distributions
- ORELA Math: Continuous Probability Distributions
- ORELA Math: Sampling
- ORELA Math: Regression & Correlation
- ORELA Mathematics Flashcards