1. 5.4/5.5 Conditions for Parallels Warm-up (IN) Learning Objective: to apply the converses of the theorems about parallel lines and prove lines are parallel. Write the converse of each statement. 1. If it rains today, we will stay inside. 2. If a quadrilateral is a square, then it is a rhombus. 3. If today is Friday, then pizza is served for lunch. 4. If a quadrilateral has four right angles, it is a rectangle. If we stay inside, it will rain today. If a quadrilateral is a rhombus, then it is a square. If pizza is served for lunch, then today is Friday. If a quadrilateral is a rectangle, then it has four right angles.

2. Notes Learning Objective: to apply the converses of the theorems about parallel lines and prove lines are parallel. **Converses of the Parallel lines theorems Corresponding angles - Alternate interior angles - Same-side interior angles - lines

3. Learning Objective: to apply the converses of the theorems about parallel lines and prove lines are parallel, and to construct parallel lines. Ex 1 – Find the value of x that will allow you to prove that WXYZ is a trapezoid. X Y W Z B (9x-25) (4x+15) lines 9x-25 = 4x+15 5x = 40 x =8 Ex 2 – Prove that if 2 sides of a quad. are parallel, and one pair of opposite angles are congruent, then the quad. is a parallelogram. F O R T Given: Prove: OR//FT FORT is a parallelogram

4. F O R T Given: Prove: OR//FT FORT is a parallelogram Statements Reasons 1. OR//FT 1. Given 6. FORT is a parallelogram 2. Def cong. 3. 4. Subst. 5. 6. Def parallelogram 5. OF//RT lines

5. **2 more ways to prove lines parallel! Dual Perpendiculars Theorem - In a plane, if 2 lines are both perpendicular to a 3 rd line, then the 2 lines are parallel. m n t Dual Parallels Theorem - m n t If 2 lines are both parallel to a 3 rd line, then the 2 lines are parallel.

6. HW – p. 245 #1-7, 16 p. 253 #1-3, 7-10,23 Out – What do you use the converses of the parallel lines theorems for? Summary – I might still need help on…. Quiz tomorrow!!!