About This Chapter
COOP Exam: Triangles - Chapter Summary
The lessons in this chapter are designed to help you understand and apply problem-solving practices regarding triangles. You can review processes for solving perimeter, area and angles, in addition to classifying and defining triangles. The following topics are reviewed in these lessons:
- Identifying the parts and properties of a triangle
- Classifying types of triangles
- Solving specific triangle problems
- Identifying similar triangles
- Constructing and illustrating triangles
- Discussing concurrent lines in a triangle
- Defining median, altitude, and angle bisector
- Applying concepts to solve problems regarding other shapes
Short, fun videos and visual examples can be helpful in retaining the material addressed in these lessons. Accompanying quizzes are used to gauge what you have retained and areas in which you need further review.
COOP Exam: Triangles Chapter Objectives
Mastering the material covered in the Triangles chapter can assist you in taking the mathematical portion of the COOP's achievement component. The math portion covers reasoning, functions, patterns, relations, and other concepts.
The paper-based exam includes 180 multiple-choice questions and is given to New Jersey students in 8th grade who are looking to enter a Catholic High school. When scores are compared to those of same-grade students, a 'good' score is considered in the 50th-74th percentile, with 'very strong' scores at or above the 75th percentile.
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. 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.
3. 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.
4. 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.
5. 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.
6. 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.
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. 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.
9. 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.
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Other chapters within the COOP Exam - New Jersey: Practice & Study Guide course
- COOP Exam: Sequences & Analogies
- COOP Exam: Quantitative Reasoning
- COOP Exam: Verbal Reasoning & Word Meaning
- COOP Exam: Reading Interpretation & Analysis
- COOP Exam: Reading Comprehension & Language Expression
- COOP Exam: Numbers & Arithmetic Operations
- COOP Exam: Integers
- COOP Exam: Irrational & Rational Numbers
- COOP Exam: Inequalities
- COOP Exam: Estimation
- COOP Exam: Decimals
- COOP Exam: Fractions
- COOP Exam: Percent
- COOP Exam: Ratios, Rates & Proportion
- COOP Exam: Square Roots
- COOP Exam: Exponents & Exponential Expressions
- COOP Exam: Scientific Notation
- COOP Exam: Measurement
- COOP Exam: Introduction to Geometry
- COOP Exam: Geometric Shape Properties
- COOP Exam: Symmetry, Similarity & Congruence
- COOP Exam: Properties of Lines
- COOP Exam: Graphing Basics
- COOP Exam: Transformations
- COOP Exam: Triangle Theorems & Proofs
- COOP Exam: The Pythagorean Theorem
- COOP Exam: Tables, Charts & Graphs
- COOP Exam: Data Analysis & Statistics
- COOP Exam: Probability & Permutations
- COOP Exam: Math Sequences & Series
- COOP Exam: Properties of Functions
- COOP Exam: Graphing Functions
- COOP Exam: Mathematical Reasoning
- COOP Exam - New Jersey Flashcards