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Questions and Answers
What can be concluded if same-side interior angles are supplementary?
What can be concluded if same-side interior angles are supplementary?
- The lines intersect.
- The lines are parallel. (correct)
- The angles are congruent.
- The lines are perpendicular.
Which theorem states that alternate interior angles are congruent if lines are parallel?
Which theorem states that alternate interior angles are congruent if lines are parallel?
- Same-Side Interior Angles Postulate
- Converse of Corresponding Angles Theorem
- Alternate Exterior Angles Theorem
- Alternate Interior Angles Theorem (correct)
According to the Triangle Angle-Sum Theorem, the angles in a triangle add up to what total?
According to the Triangle Angle-Sum Theorem, the angles in a triangle add up to what total?
- 270 degrees
- 90 degrees
- 360 degrees
- 180 degrees (correct)
What is the slope of a line between two points given by the coordinates $(x_1, y_1)$ and $(x_2, y_2)$?
What is the slope of a line between two points given by the coordinates $(x_1, y_1)$ and $(x_2, y_2)$?
If corresponding angles are congruent, what can be inferred about the lines?
If corresponding angles are congruent, what can be inferred about the lines?
Which theorem would you use to prove that lines are parallel if alternate exterior angles are congruent?
Which theorem would you use to prove that lines are parallel if alternate exterior angles are congruent?
What equation represents the slope-intercept form of a line?
What equation represents the slope-intercept form of a line?
What is the relationship between alternate interior angles and parallel lines?
What is the relationship between alternate interior angles and parallel lines?
When using the Triangle Exterior Angles Theorem, what does the exterior angle equal?
When using the Triangle Exterior Angles Theorem, what does the exterior angle equal?
Which theorem can be applied to show that if corresponding angles are congruent, then the lines are parallel?
Which theorem can be applied to show that if corresponding angles are congruent, then the lines are parallel?
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Study Notes
Parallel Lines
- Parallel lines do not intersect at any point.
- Key theorems apply when the lines are confirmed as parallel:
- Same-Side Interior Angles Postulate: If lines are parallel, same-side interior angles are supplementary.
- Alternate Interior Angles Theorem: If lines are parallel, alternate interior angles are congruent.
- Corresponding Angles Theorem: If lines are parallel, corresponding angles are congruent.
- Alternate Exterior Angles Theorem: If lines are parallel, alternate exterior angles are congruent.
Proving Lines are Parallel
- Specific theorems assist in proving that lines are parallel:
- Converse of Same-Side Interior Angles Postulate: If same-side interior angles are supplementary, the lines are parallel.
- Converse of Alternate Interior Angles Theorem: If alternate interior angles are congruent, the lines are parallel.
- Converse of Corresponding Angles Theorem: If corresponding angles are congruent, the lines are parallel.
- Converse of Alternate Exterior Angles Theorem: If alternate exterior angles are congruent, the lines are parallel.
Triangle Angle-Sum Theorem
- The sum of the three interior angles of a triangle equals 180 degrees.
Triangle Exterior Angles Theorem
- The exterior angle of a triangle is equal to the sum of the two remote interior angles.
Slope Information
- Slope Formula:
- ( m = \frac{y_2 - y_1}{x_2 - x_1} )
- Slope-Intercept Form:
- ( y = mx + b )
- Point-Slope Form: Equation not explicitly mentioned, but generally represented as ( y - y_1 = m(x - x_1) ).
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