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.