Unit 5 Intersecting and Parallel lines

5.1/5.2

linear pair: angles a+b=180 degrees (supplementary) and share one common side and vertex. The non-common sides are opposite rays. (MUST SHARE A SIDE TO BE LINEAR PAIR) Reason: Linear pair

Vertical Angles: angles a=b. Share common vertex, both sides are opposite rays. Reason: Vertical ∠s are ≅

Perpendicular lines: Straight lines that intersect with each other and form 4 angles, each of which measures 90 degrees. Reason: Df.: ⊥

5.3

5.4 (proving parallel lines)

5.5(properties of parallel lines)

Corresponding angles: On same side of transversal, same side of the two lines intersecting with the transversal.

Alternate Interior angles: On seperate sides of transversal, seperate sides of the two lines intersecting with the transversal (between)

Consecutive interior angles: on same side of transversal, same side of two lines intersecting with the transversal (between).

Corr.∠s ≌ ⇒// lines

Alt.int.∠s ≌ ⇒// lines

Co-int.∠s supp. ⇒ // lines

Opposite of 5.4, if two lines are parallel, then what the angles will become.

// lines ⇒ Corr.∠s ≌

// lines ⇒ Alt.int.∠s ≌

// lines ⇒ Co-int. ∠s supp.

Other Important Reasons

Given, Constructed: What the question gives (evidence), and what you have drawn (added on the diagram)

Addition, Subtraction: When you add/subtract. Example : 1. mm∠1+m∠2=180 | 1. Addition

Transitivity of // lines: if two lines are parallel to the same line, than these two lines are also parallel.

Area of a △: Area formula of a triangle, 1/2 x base x height

Intersection angle: the angle of where two lines intersect (夹角). Smaller or equal to 90 degrees.