Transcript Day_Three
Warm Ups 1. Find the missing perimeter. P = ? mm 3 6 P = 25 mm 2. Solve for x. 12 8 x Section 6.6 Use Proportionality Theorems Isn’t logic a beautiful thing! Activity B In the diagram, DE | | AC. D 1. Name a pair of similar A triangles and explain why they are similar. E C Activity B In the diagram, DE || AC. D 1. Name a pair of similar triangles and explain E C A B why they are similar. B D E A C Activity B 3. Write a proportion & solve for x. 10 848 4. What is the ratio BD: DA? Reduce your answer. 5. What is the ratio BE: EC ? Reduce your answer. 6. What do you notice? 60 D E 636 x C A 8 86 10 10 x Proportionality Theorems! Theorem 6.4 Triangle Proportionality Theorem If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally. Example 1 Find the length of YZ. Proportionality Theorems! Theorem 6.5 Converse of the Triangle Proportionality Theorem If a line divides two sides of a triangle proportionally, then it is parallel to the third side. Example 2 Determine whether PS || QR. Example 3 Find the value of x so that BC || ED . Discussion Recall that the distance between two parallel lines is always equal. This distance, however, must be measured along a perpendicular segment. CD EF Discussion But what if the distance is not perpendicular? D A Are these lengths still equal? Or does some E B other relationship exist? F C Proportionality Theorems! Theorem 6.6 If three parallel lines intersect two transversals, then they divide the transversals proportionally. Example 4 Find the length of AB. Discussion Notice that the angle bisector also divides Recall angle the that thirdan side of the bisector a ray triangle is into twothat parts. divides an angle Are those parts into two congruentOr parts. congruent? is there some other relationship between A them? B D C Proportionality Theorems! Theorem 6.7 Angle Bisector Proportionality Theorem If a ray bisects an angle of a triangle, then it divides the opposite side into segments whose lengths are proportional to the other two sides. Example 5 Find the value of x. Example 6 Find the value of x. Assignment