1. 7-4: Parallel Lines and Proportional Parts Expectation: G1.1.2: Solve multi-step problems and construct proofs involving corresponding angles, alternate interior angles, alternate exterior angles, and same-side (consecutive) interior angles. G1.2.2: Construct and justify arguments and solve multi- step problems involving angle measure, side length, perimeter, and area of all types of triangles. G2.3.4: Use theorems about similar triangles to solve problems with and without use of coordinates.

2. Given that ΔXYZ is similar to ΔABC, what is the sum of the lengths of sides XY and XZ in ΔXYZ below? A. 9 B. 12 C. 15 D. 24 E. 27 X y Z 9 Y z A 5 C 3 B 4

3. Triangle Proportionality Theorem (Side Splitting Theorem) If a line is parallel to a side of a triangle and intersects the other 2 sides in distinct points, then it splits those 2 sides into segments of proportional length.

4. Triangle Proportionality Theorem A E D C B If DE || AC, AD BD CE BE =

5. 4 common proportions from the side splitting theorem w z y x

6. Determine the value of x below if EB || CD. A E B DC 4 x 3 5

7. In the diagram below, segments that appear to be parallel are parallel. Solve for x. x 15 24 12

8. In the figure below, segment AB is parallel to segment CD. What is the sum of AC and BD? A. 3 ⅓ B. 4 ⅓ C. 5 ⅓ D. 7 ⅔ E. 8 ⅔ A C E D B 3 2 8 5

9. Converse of Triangle Proportionality Theorem If a line intersects two sides of a triangle in distinct points and separates the sides into proportional segments, then the line is parallel to the third side of the triangle.

10. A E D C B If AB DE, then AE || BD. = BCDC

11. Is AC || DE? B 6E6 8 D A 2 C

12. True or False? Justify If BE = 3 / 5 AB, then DC = 2 / 5 BC. A E B D C

13. Midpoint Connector Theorem If a segment’s endpoints are the midpoints of 2 sides of a triangle, then it is parallel to and half the length of the third side.

14. Midpoint Connector Theorem A E D C B E and D are the midpoints of their respective sides so ED || AB and AB = 2ED

15. Proportional Transversals Corollary If 3 or more parallel lines intersect 2 transversals, then they cut the transversals proportionally.

16. Proportional Transversals Corollary s t l m n a b y z If l || m and m || n, then. a b y z =

17. Find the values of all of the variables below if w + x + y + z = 20 w x y z 6354

18. Congruent Transversal Segment Theorem If 3 or more parallel lines cut off congruent segments on one transversal, then they cut congruent segments on every transversal.

19. Solve for x l m n ut x 12

20. Assignment pages 367 – 369, # 13 -29 (odds), 39 and 41 (odds)