Podcast Beta
Questions and Answers
Which angles are on the same side of the transversal?
What type of angles are opposite each other at an intersection?
Why are vertical angles always congruent?
When are corresponding angles always congruent?
Signup and view all the answers
Which type of angles must be 90 degrees for consecutive interior angles to be congruent?
Signup and view all the answers
What is the condition for alternate angles to be congruent?
Signup and view all the answers
How do consecutive exterior angles relate to each other?
Signup and view all the answers
What do vertical angles share?
Signup and view all the answers
'Lines are also called straight angles because they always form a _____ angle.'
Signup and view all the answers
Are consecutive interior angles always congruent?
Signup and view all the answers
Study Notes
Angle Basics
- An angle is defined as the amount of turn between two lines, segments, or rays.
- Common types of angles include acute, obtuse, right, straight, and reflex angles.
- Acute angles are under 90 degrees, obtuse angles are greater than 90 degrees, and right angles are exactly 90 degrees.
- Straight angles are 180 degrees, and reflex angles are greater than 180 degrees but less than 360 degrees.
Angle Relationships
- Two angles together can form special circumstances:
- Complementary angles: add up to 90 degrees.
- Supplementary angles: add up to 180 degrees.
Angle Relationships with Intersecting Lines
- When two lines intersect with a third line, eight angles are formed.
- There are six types of angle relationships:
- Corresponding angles
- Alternate angles (interior and exterior)
- Consecutive angles (interior and exterior)
- Vertical angles
Corresponding Angles
- Corresponding angles are angles in the same relative positions at each intersection.
- There are four pairs of corresponding angles.
- Corresponding angles cannot be all interior or all exterior, as one angle will always be interior and the other exterior.
Alternate Angles
- Alternate angles are formed when two lines are intersected by a third transversal line.
- There are two types of alternate angles:
- Alternate interior angles: between the two lines being intersected and on opposite sides of the transversal.
- Alternate exterior angles: outside the two lines being intersected and on opposite sides of the transversal.
Consecutive Angles
- Consecutive angles are angles on the same side of the transversal.
- There are two pairs of consecutive interior angles and two pairs of consecutive exterior angles.
Vertical Angles
- Vertical angles are angles that are opposite each other at an intersection.
- Vertical angles are always congruent and share the vertex but not any sides.
Congruent Angles
- Angles are congruent when they have the same measurement.
- Vertical angles are always congruent.
- Corresponding angles are congruent when the two lines being intersected by the transversal are parallel.
- Alternate angles are congruent only when the two lines being intersected by a transversal are parallel.
- Consecutive interior angles are congruent only when the transversal intersects two parallel lines at 90 degrees.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge of angles in geometry with this quiz! Explore different types of angles such as acute, obtuse, right, straight, and reflex angles. Learn about the amount of turn between lines, segments, or rays.
