Vertical Angles
Vertical angles are a pair of non-adjacent angles formed by the intersection of two lines. When two lines intersect, they form four angles. The pairs of angles opposite each other are called vertical angles. Vertical angles are always congruent, which means they have the same measure.
Properties of Vertical Angles:
- Vertical angles are always congruent.
- Vertical angles are formed by the intersection of two lines.
- Vertical angles are non-adjacent angles.
- The sum of the measures of vertical angles is always 180 degrees.
Examples:
Let's consider two intersecting lines, line AB and line CD. The angles formed are angle 1, angle 2, angle 3, and angle 4. Angle 1 and angle 3 are vertical angles, as are angle 2 and angle 4. Angle 1 and angle 3 are congruent, as are angle 2 and angle 4.
Study Guide:
When working with vertical angles, remember the following key points:
- Vertical angles are always congruent.
- Vertical angles are formed by the intersection of two lines.
- Vertical angles are non-adjacent angles.
- The sum of the measures of vertical angles is always 180 degrees.
Practice identifying and solving problems involving vertical angles to strengthen your understanding of this concept.
[Vertical Angles] Related Worksheets and Study Guides:
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The resources above cover the following skills:
Number and Operations (NCTM)
Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
Understand the place-value structure of the base-ten number system and be able to represent and compare whole numbers and decimals.
Use models, benchmarks, and equivalent forms to judge the size of fractions.
Recognize and generate equivalent forms of commonly used fractions, decimals, and percents.
Algebra (NCTM)
Use mathematical models to represent and understand quantitative relationships.
Model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions.