Objectives: Identify parallel and perpendicular lines Identify the relationships of angles formed by parallel lines and a transversal
Line Relationships Parallel Lines: are lines that are coplanar and do not intersect Perpendicular Lines: are lines that are coplanar and intersect at a right angle
Angle Relationships Complementary Angles - are two angles that add up to 90° Supplementary Angles - are angles that add up to 180° (form a straight angle) Vertical Angles - are the angles opposite each other when two lines cross.
Transversal A transversal is a line that intersects two or more lines at different points Line t is a transversal.
Parallel Lines cut by a Transversal List the relationships you can see with the angles above.
Angles Formed by Transversals Angles are corresponding angles if they occupy corresponding positions.
Corresponding Angles When two parallel lines are cut by a transversal, the resulting corresponding angles are congruent. So, in the figure above, if l || m, then ∠1 ≊∠ 2. Source: hotmath.com
Angles Formed by Transversals Angles are alternate exterior angles if they lie outside the parallel lines on opposite sides of the transversal.
Alternate Exterior Angles When two parallel lines are cut by a transversal, the resulting alternate exterior angles are congruent. So, in the figure above, if k || l, then: ∠1 ≊ ∠7 and ∠4 ≊ ∠6. Source: hotmath.com
Angles formed by Transversals Alternate interior angles lie on the inside of the parallel lines on opposite sides of the transversal.
Alternate Interior Angles When two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent. So, in the figure above, if k || l, then ∠2 ≊ ∠8 and ∠3 ≊ ∠5. Source: hotmath.com
Angles formed by Transversals Consecutive interior angles lie inside of the parallel lines on the same side of the transversal.
Consecutive Interior Angles If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary. So, in the figure above, if l || m, then ∠3 + ∠5 = 180° and ∠4 + ∠6 = 180°.