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  1. Practice Open-Ended (10 mins) Discounts & Sales Tax Sports Authority is having a sale. Every item in the store is discounted, however the discounts vary throughout the store! 1.) A jacket in the women’s clothing department is regularly priced at $60 and is on sale for $42. Determine the percent discount rate for this item. 2.) Find the total cost for a Nike tennis racket that is regularly priced at $125 and is on sale for 15% off. (*include a 6% sales tax.) 3.) If all of the sneakers are on sale at the % discount ratein #2, and the sales price for a pair of Nike sneakers is $85 (not including tax), what was the original price of the sneakers?

  2. Lesson 4Parallel Lines & Transversals

  3. Parallel Lines and Transversals What would you call two lines which do not intersect? Parallel A solid arrow placed on two lines of a diagram indicate the lines are parallel. Exterior Interior The symbol || is used to indicate parallel lines. Exterior AB || CD

  4. Parallel Lines and Transversals A slash through the parallel symbol || indicates the lines are not parallel. AB || CD

  5. Parallel lines Non-Parallel lines transversal transversal Transversal A line, ray, or segment that intersects 2 or more COPLANAR lines, rays, or segments. Exterior Exterior Interior Interior Exterior Exterior

  6. Parallel Lines and Transversals Transversal - A transversal is a line which intersects two or more lines in a plane. The intersected lines do not have to be parallel. Lines j, k, and m are intersected by line t. Therefore, line t is a transversal of lines j, k, and m.

  7. exterior interior exterior INTERIOR –The space INSIDE the 2 lines EXTERIOR -The space OUTSIDE the 2 lines

  8. 1 2 3 4 5 6 7 8 Special Angle Relationships Interior Angles <3 & <6 are Alternate Interior angles <4 & <5 are Alternate Interior angles <3 & <5 are Same Side Interior angles <4 & <6 are Same Side Interior angles Exterior Interior Exterior Exterior Angles <1 & <8 are Alternate Exterior angles <2 & <7 are Alternate Exterior angles <1 & <7 are Same Side Exterior angles <2 & <8 are Same Side Exterior angles

  9. 1 2 3 4 6 5 7 8 If the lines are not parallel, these angle relationships DO NOT EXIST. Special Angle RelationshipsWHEN THE LINES ARE PARALLEL ♥Alternate Interior Angles are CONGRUENT ♥Alternate Exterior Angles are CONGRUENT ♥Same Side Interior Angles are SUPPLEMENTARY ♥Same Side Exterior Angles are SUPPLEMENTARY Exterior Interior Exterior

  10. Corresponding Angles & Consecutive Angles Corresponding Angles: Two angles that occupy corresponding positions.  2  6, 1  5,3  7,4  8 Exterior 1 2 3 4 Interior 5 6 7 8 Exterior

  11. L Line L G Line M P A B Line N Q D E F Corresponding Angles When two parallel lines are cut by a transversal, pairs of corresponding angles are formed. ÐGPB = ÐPQE ÐGPA = ÐPQD ÐBPQ = ÐEQF ÐAPQ = ÐDQF Four pairs of corresponding angles are formed. Corresponding pairs of angles are congruent.

  12. Same Side Interior/Exterior Angles Same Side Interior Angles: Two angles that lie between parallel lines on the same sides of the transversal. Same Side Exterior Angles: Two angles that lie outside parallel lines on the same sides of the transversal. m3 +m5 = 180º, m4 +m6 = 180º Exterior 1 2 m1 +m7 = 180º, m2 +m8 = 180º 3 4 Interior 5 6 7 8 Exterior

  13. L Line L G Line M P A B Line N Q D E F Interior Angles The angles that lie in the area between the two parallel lines that are cut by a transversal, are calledinterior angles. Exterior ÐBPQ + ÐEQP = 1800 600 1200 Interior 1200 600 ÐAPQ + ÐDQP = 1800 Exterior The measures of interior angles in each pairadd up to 1800. A pair of interior angles lie on thesame sideof the transversal.

  14. Alternate Interior/Exterior 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 2  7,1  8 1 2 Exterior 3 4 Interior 5 6 7 8 Exterior

  15. L Line L G Line M P A B Line N Q D E F Alternate Interior Angles Alternate angles are formed on opposite sides of the transversal and at different intersecting points. ÐBPQ = ÐDQP ÐAPQ = ÐEQP Two pairs of alternate angles are formed. Pairs of alternate angles are congruent.

  16. 1 2 3 4 6 5 7 8 Let’s Practice m<1=120° Find all the remaining angle measures. 120° 60° 120° 60° 120° 60° 120° 60°

  17. Another practice problem Find all the missing angle measures, and name the postulate or theorem that gives us permission to make our statements. 40° 180-(40+60)= 80° 60° 80° 60° 40° 80° 120° 100° 60° 80° 120° 60° 100°

  18. Line L G Line M P A B 500 Line L G 1300 Line M Line N A P B Q E D Line L G F Line N Q D E Line M P A B F Line N Q E D F Name the pairs of the following angles formed by a transversal. Test Yourself Corresponding angles Alternate angles Interior angles

  19. Department Store A department store is divided into two sections, electronics and furniture. Each section offers a discount rate; items in the same section sell at the same discount rate, but not necessarily at the same price. A.) One of the items in the electronics section has an original price $120 and a sale price of $102. One of the items in the furniture section has an original price of $60 and a sale price of $48. Determine the (percent) discount rate in the electronics section and the (percent) discount rate in the furniture section. Show your work. B.) Using the discount rate found in part A, find the total amount, including a 6% sales tax, that Andrew paid for an electric item and a furniture item if the original price of each of these items $200. Show your work. C.) Andrew plans to buy an office lamp from the furniture section and a laptop computer from the electronic section of this department store. The original price of the laptop computer is $1,350. The original price of the office lamp is $89. Andrew is thinking of two methods to find the total amount he will save (not including the tax). The two methods are stated below: Method I: Find the discount on the laptop and find the discount on the lamp. Find the sum of the two discounts Method II: Find the sum of the original prices of the two items. Find the average of the discount rates from part A Use the average rate to find the discount on the sum. Would Andrew’s results be the same using both methods? Show your work to explain your answer.