Parallel Lines & Angles PDF

3.3 Notes: Parallel lines and angle formed by transversals Learning Target: Prove and use theorems about parallel lines cut by transversals  Learning Target: Prove and use theorems about parallel lines cut by transversals Theorem If two paralle...

3.3 Notes: Parallel lines and angle formed by transversals Learning Target: Prove and use theorems about parallel lines cut by transversals  Learning Target: Prove and use theorems about parallel lines cut by transversals Theorem If two parallel lines are cut by a transversal, then alternate interior angles are congruent. If… Then… ∠4 ≅ ∠6 ℓ"m ∠3 ≅ ∠5  Learning Target: Prove and use theorems about parallel lines cut by transversals Using the figure shown and given that m∠3 = 55! , find the measure of each angle. Tell what theorem or postulate you used. (Recall that red arrow head notation means || lines.) 1250550 1250 550 150 550,2 so a. m∠5 55 b. m∠7 58 c. m∠4 725 d. m∠2 125  Learning Target: Prove and use theorems about parallel lines cut by transversals Theorem If two parallel lines are cut by a transversal, then corresponding angles are congruent. If… Then… ∠1 ≅ ∠5 ℓ"m ∠2 ≅ ∠6 ∠3 ≅ ∠7 ∠4 ≅ ∠8  Learning Target: Prove and use theorems about parallel lines cut by transversals Theorem If two parallel lines are cut by a transversal, then same-side interior angles are supplementary. If… Then… ℓ"m m∠4 + m∠5 = 180! m∠3 + m∠6 = 180!  Learning Target: Prove and use theorems about parallel lines cut by transversals Theorem If two parallel lines are cut by a transversal, then alternate exterior angles are congruent. If… Then… ∠1 ≅ ∠7 ℓ"m ∠2 ≅ ∠8  Learning Target: Prove and use theorems about parallel lines cut by transversals Given the figure shown and m∠4 = 42! , find the measures of the other angles. 420 138 138 42 42 138 138 420 180 v2  Learning Target: Prove and use theorems about parallel lines cut by transversals Using the figure shown, what are the measures of angle 3 and angle 4? Which theorem justifies each answer? iiiiii air 750 750 180 105 15 Learning Target: Prove and use theorems about parallel lines cut by transversals Given the figure and l || m, find the value of x. 1. Find the value of x and y in the following figure. 18 y 39 21y 16 15x 24 20x 19 2. Find x, y, and z in the following figure. 4x2 5 13x 7 z y 3. Find the measures of 1, 2, 3, and 4 in the figure below. 1 (8x – 3) (x + 15) 2 (2x + 6) 3 (4x – 5) 4 4. Find the value of x and y in the following figure. 14y + 5 17x + 1 23x – 9 8y – 5