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Understand angles, parallel lines, intersecting lines, transversals, and relationship between different angle pairs in a fun and interactive way. Practice finding missing angle measures and explore concepts like vertical angles and linear pairs.
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Angles and Parallel Lines MCC8.G.5
Intersecting Lines • Lines that cross at exactly one point. • Think of an intersection, where two roads cross each other.
Perpendicular Lines • Lines that intersect to form right angles.
B A D l C m PARALLEL LINES • Definition: lines that do not intersect. • Think: railroad tracks! • Here’s how it looks: • This is how you write it:l || m AB|| CD • This is how you say it: “Line l is parallel to line m” and “Line AB is parallel to line CD”
Examples of Parallel Lines • Hardwood Floor • Opposite sides of windows, desks, etc. • Parking slots in parking lot • Parallel Parking • Streets
Examples of Parallel Lines • Streets: Belmont & School
Transversal • Definition: A line that intersects two or more lines in a plane at different points is called a transversal. • Line t is a transversal here, because it intersects line m and line n. t m n
Vertical Angles & Linear Pair Vertical Angles: Linear Pair: Two angles that are opposite angles. Vertical angles are congruent, which means they’re equal. • 1 4, 2 3, 5 8, 6 7 (The symbol means congruent, in case you’ve forgotten) Supplementary angles that form a line (sum = 180) These are linear pairs: 1 & 2 ,2 & 4 , 4 &3, 3 & 1, 5 & 6,6 & 8, 8 & 7, 7 & 5 1 2 3 4 5 6 7 8
t 1 2 4 3 6 5 7 8 Linear Pairs • Two (supplementary and adjacent) angles that form a line (sum=180) • 1+2=180 • 2+4=180 • 4+3=180 • 3+1=180 • 5+6=180 • 6+8=180 • 8+7=180 • 7+5=180
Can you… Find the measures of the missing angles? t ? 108 72 180 - 72 ? 108
Complementary Angles • Two angles whose measures add to 90˚.
Adjacent Angles • Angles in the same plane that have a common vertex and a common side.
Angles and Parallel Lines • If two parallel lines are cut by a transversal, then the following pairs of angles are congruent. • Corresponding angles • Alternate interior angles • Alternate exterior angles • If two parallel lines are cut by a transversal, then the following pairs of angles are supplementary. • Consecutive interior angles • Consecutive exterior angles Continued…..
Corresponding Angles Corresponding Angles: Two angles that occupy corresponding positions. 2 6, 1 5,3 7,4 8 1 2 3 4 5 6 7 8
Consecutive Angles Consecutive Interior Angles: Two angles that lie between parallel lines on the same sides of the transversal. (Think “interior” as in, inside the parallel lines…) Consecutive Exterior Angles: Two angles that lie outside parallel lines on the same sides of the transversal. m3 +m5 = 180º, m4 +m6 = 180º 1 2 m1 +m7 = 180º, m2 +m8 = 180º 3 4 5 6 7 8
Alternate Angles • Alternate Interior Angles: Two angles that lie between parallel lines on opposite sides of the transversal (but not a linear pair). • Alternate Exterior Angles: Two angles that lie outside parallel lines on opposite sides of the transversal. 3 6,4 5 1 2 3 4 2 7,1 8 5 6 7 8
B A 1 2 10 9 12 11 4 3 C D 5 6 13 14 15 16 7 8 s t Example:If line AB is parallel to line CD and s is parallel to t, find the measure of all the angles when m< 1 = 100°. Justify your answers. Hint: First, find angle 2! Use the measure of angle 1 to get your started. m<2=80° m<3=100° m<4=80° m<5=100° m<6=80° m<7=100° m<8=80° m<9=100° m<10=80° m<11=100° m<12=80° m<13=100° m<14=80° m<15=100° m<16=80°
B A 1 2 10 9 12 11 4 3 C D 5 6 13 14 15 16 7 8 s t Example: If line AB is parallel to line CD and s is parallel to t, find: 1. the value of x, if m<3 = 4x + 6 and the m<11 = 126. 2. the value of x, if m<1 = 100 and m<8 = 2x + 10. 3. the value of y, if m<11 = 3y – 5 and m<16 = 2y + 20. ANSWERS: 1. 30 2. 35 3. 33
