Entry Task If ∠ YDF = 121 and DR bisects ∠ FDI find the measure of: a)∠ IDA b)∠ YDA c)∠ RDI Y D A F R I
Properties of Parallel Lines 3.2 Learning Target: I can use parallel lines to prove angle relationships Success Criteria: I can find the measures of angles formed by parallel lines crossed by a transversal. I can prove angles congruent using the theorems and properties of parallel lines crossed by a transversal
Parallel Lines Using the 2 parallel lines, draw a transversal that intersects both lines. Predict, based on visual inspection connections about angle pairs – Corresponding – Alternate Exterior – Alternate Interior – Same Side Interior Angles Compare your findings with your table partners Measure all 8 angles using a protractor On your paper, compare your predictions to your measurements
Parallel Lines Cont….. Make a general statement about each angle pair Share with your table partner each of the four statements Assign an angle pair to each student Move to correct corner of room and share with new group Create a General Statement on an 8x11 piece of paper for our Public Record
Proving Lines Parallel Watch this Video firstVideo Then watch this VideoVideo
Check It Out! Example 1 Find m QRS. m QRS = 180° – x x = 118 m QRS + x = 180° Corr. s Post. = 180° – 118° = 62° Subtract x from both sides. Substitute 118° for x. Def. of Linear Pair
Find each angle measure. Example 2: Using the Corresponding Angles Postulate A. m ECF x = 70 B. m DCE m ECF = 70° Corr. s Post. 5x = 4x + 22 Corr. s Post. x = 22Subtract 4x from both sides. m DCE = 5x = 5(22)Substitute 22 for x. = 110°
Find each angle measure. Example 3: Finding Angle Measures A. m EDG B. m BDG m EDG = 75°Alt. Ext. s Thm. m BDG = 105° x – 30° = 75° Alt. Ext. s Thm. x = 105Add 30 to both sides.
Check It Out! Example 4 Find m ABD. m ABD = 2(25) + 10 = 60° 2x + 10° = 3x – 15° Alt. Int. s Thm. Subtract 2x and add 15 to both sides. x = 25 Substitute 25 for x.
Same as #1
Homework Homework P. 153 #7-10, 12-20,22 Challenge - 28