Geometry
Parallel and Perpendicular Lines flashcards
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- What are parallel lines?Lines and Transversals
- Distinct coplanar lines that never intersect.
- What are perpendicular lines?Lines and Transversals
- Lines intersecting at right angles.
- Can two distinct coplanar lines both intersect and be parallel?Lines and Transversals
- No.
- What is the measure of an angle formed by perpendicular lines?Lines and Transversals
- 90°.
- Do nonperpendicular intersecting lines make a right angle?Lines and Transversals
- No.
- What is a transversal?Lines and Transversals
- A line intersecting two or more coplanar lines at distinct points.
- Where are interior angles?Lines and Transversals
- Between the two crossed lines.
- Where are exterior angles?Lines and Transversals
- Outside the two crossed lines.
- How many intersections are needed to compare angles along a transversal?Lines and Transversals
- At least two.
- Can a transversal cross nonparallel lines?Lines and Transversals
- Yes.
- Corresponding angles occupy what positions?Lines and Transversals
- Matching positions at the two intersections.
- Where are alternate interior angles?Lines and Transversals
- Between the lines, on opposite sides of the transversal.
- Where are alternate exterior angles?Lines and Transversals
- Outside the lines, on opposite sides of the transversal.
- Are same-side interior angles alternate?Lines and Transversals
- No; they lie on the same side.
- Do angle position names alone prove lines are parallel?Lines and Transversals
- No.
- Parallel lines make corresponding angles what?Angle Relationships with Parallel Lines
- Congruent.
- If a corresponding angle is 72°, the other is?Angle Relationships with Parallel Lines
- 72°.
- What condition supports corresponding-angle congruence?Angle Relationships with Parallel Lines
- The crossed lines are parallel.
- Do corresponding angles sum to 180° generally?Angle Relationships with Parallel Lines
- No; they are equal when lines are parallel.
- What theorem finds matching-corner measures?Angle Relationships with Parallel Lines
- Corresponding Angles Theorem.
- Parallel lines make alternate interior angles what?Angle Relationships with Parallel Lines
- Congruent.
- Parallel lines make alternate exterior angles what?Angle Relationships with Parallel Lines
- Congruent.
- Alternate angles lie on which sides of transversal?Angle Relationships with Parallel Lines
- Opposite sides.
- Are alternate exterior angles between the lines?Angle Relationships with Parallel Lines
- No.
- An alternate interior angle is 60°. Its partner?Angle Relationships with Parallel Lines
- 60°.
- Same-side interior angles total?Angle Relationships with Parallel Lines
- 180° when the crossed lines are parallel.
- Are same-side interior angles congruent in general?Angle Relationships with Parallel Lines
- No.
- Partner to 110° same-side interior angle?Angle Relationships with Parallel Lines
- 70°.
- What does supplementary mean?Angle Relationships with Parallel Lines
- Angle measures sum to 180°.
- Where are same-side interior angles?Angle Relationships with Parallel Lines
- Between the lines on the same side of transversal.
- Corresponding Angles Converse says?Proving Lines Parallel
- Equal corresponding angles imply parallel lines.
- Does one drawing that looks parallel prove it?Proving Lines Parallel
- No.
- What must a transversal do for the converse?Proving Lines Parallel
- Cut the two coplanar lines at distinct points.
- Are corresponding positions at separate intersections?Proving Lines Parallel
- Yes.
- What conclusion follows from congruent corresponding angles?Proving Lines Parallel
- The crossed lines are parallel.
- Alternate Interior Angles Converse says?Proving Lines Parallel
- Congruent alternate interior angles imply parallel lines.
- Alternate Exterior Angles Converse says?Proving Lines Parallel
- Congruent alternate exterior angles imply parallel lines.
- What conclusion can equal alternate angles justify?Proving Lines Parallel
- Parallel lines.
- Do alternate angles lie on the same side?Proving Lines Parallel
- No.
- Can the converse test use equal interior angles on opposite sides?Proving Lines Parallel
- Yes.
- Same-Side Interior Converse says?Proving Lines Parallel
- Supplementary same-side interior angles imply parallel lines.
- What sum is required by the converse?Proving Lines Parallel
- 180°.
- Are same-side interior angles inside the pair?Proving Lines Parallel
- Yes.
- Can 80° and 100° same-side interiors prove parallel?Proving Lines Parallel
- Yes; they total 180°.
- Can 80° and 90° same-side interiors prove parallel?Proving Lines Parallel
- No; they total 170°.
- Slope formula?Slopes of Lines
- (y₂−y₁)/(x₂−x₁), when the denominator is nonzero.
- What is rise?Slopes of Lines
- Change in y.
- What is run?Slopes of Lines
- Change in x.
- Why is vertical slope undefined?Slopes of Lines
- Its horizontal change is zero.
- Does reversing both point orders change slope?Slopes of Lines
- No.
- Slope of horizontal line?Slopes of Lines
- 0.
- Slope of vertical line?Slopes of Lines
- Undefined.
- Line rising left to right has what slope?Slopes of Lines
- Positive.
- Line falling left to right has what slope?Slopes of Lines
- Negative.
- Does undefined slope mean zero slope?Slopes of Lines
- No.
- Slopes of distinct nonvertical parallel lines?Slopes of Lines
- Equal.
- Slopes of nonvertical perpendicular lines?Slopes of Lines
- Negative reciprocals.
- Product of perpendicular nonzero slopes?Slopes of Lines
- −1.
- What line is perpendicular to horizontal?Slopes of Lines
- Vertical.
- Can equal slopes alone show two equations are distinct parallel lines?Slopes of Lines
- No. Equal slopes show the lines are parallel or the same line; also check that they are not the same line (different y-intercepts).
- What does m mean in y=mx+b?Equations of Parallel and Perpendicular Lines
- Slope.
- What does b mean in y=mx+b?Equations of Parallel and Perpendicular Lines
- Y-intercept.
- Slope of y=4x+2?Equations of Parallel and Perpendicular Lines
- 4.
- Y-intercept of y=4x+2?Equations of Parallel and Perpendicular Lines
- 2.
- Two distinct parallel lines in y=mx+b share what?Equations of Parallel and Perpendicular Lines
- The same m and different b.
- Point-slope form?Equations of Parallel and Perpendicular Lines
- y−y₁=m(x−x₁).
- What information does point-slope form need?Equations of Parallel and Perpendicular Lines
- A slope and a point on the line.
- Slope in y−3=2(x−1)?Equations of Parallel and Perpendicular Lines
- 2.
- Point in y−3=2(x−1)?Equations of Parallel and Perpendicular Lines
- (1,3).
- Can point-slope form be rearranged to y=mx+b?Equations of Parallel and Perpendicular Lines
- Yes.
- Slope of a line parallel to y=3x+1?Equations of Parallel and Perpendicular Lines
- 3.
- Slope of a line perpendicular to y=3x+1?Equations of Parallel and Perpendicular Lines
- −1/3.
- What equation is a vertical line through x=4?Equations of Parallel and Perpendicular Lines
- x=4.
- What equation is a horizontal line through y=5?Equations of Parallel and Perpendicular Lines
- y=5.
- Must a parallel line through an external point have the same intercept?Equations of Parallel and Perpendicular Lines
- No; it has the same slope.