Properties of Parallel Lines Section 3-2 section 3-2

What we will cover… Corresponding Angles Alternate Interior Angles Same-side Interior Angles What we can prove. section 3-2

Corresponding Angles Corresponding angles lie in the same place with regard to the original lines and the transversal. If we take an overhead picture of the two intersections, they will lie in the same part of the picture section 3-2

Corresponding Angles on Parallel Lines When the lines are parallel… What do you think will be true of the corresponding angles here? THEY ARE CONGRUENT section 3-2

The Corresponding angles will stay congruent 1 1 2 2 section 3-2

A Proof Given: lines k and l with corresponding angles 1 and 2 Prove: m<2 = m<3 1 k 3 2 l section 3-2

Alternate Interior Angles Alternate Interior angles lie between the parallel lines and on opposite sides of the transversal. section 3-2

Alternate Interior Angles When we look at the alternate interior angles on parallel lines… What do you think about these angles? THEY ARE CONGRUENT section 3-2

Same-side Interior Angles These will be between the parallel lines on the same side of the transversal Lets take a look at the same-side interior angles… Do they look congruent? NO They are supplementary. section 3-2

What This Means When we have parallel lines cut by a transversal: Corresponding angles are congruent. Alternate interior angles are congruent. Same-side interior angles are supplementary section 3-2

Example 1: What is the value of y if lines a and b are parallel? What is the relationship between the angles? Then they must be: (y+50)° a (2y)° b Corresponding (2y) = (y+50) y = 50 Congruent section 3-2

Example 2: What is the value of x if lines p and q are parallel? What relationship do the angles have? This means they are: q (x+20)° (x–10)° p (x+20) + (x–10) = 180 2x + 10 = 180 x = 85 Same-side interior Supplementary section 3-2

What we can prove… Take a look at these angles… What do you think will be true about these? How about these angles? They are congruent They are congruent **Some texts call these alternate exterior angles. section 3-2

Theorem 3-4 If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other one also 1 m<1 = 90˚ section 3-2

Are there parallel lines here? section 3-2

Are these lines parallel? …or even straight? section 3-2

Are these lines parallel? section 3-2