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6.2 Properties of Parallelograms OBJECTIVE: To discover properties of parallelograms Use parallel lines (If lines are parallel, same-side interior angles are ________________________ ) to find the missing angles in the parallelogram below: C-28: The consecutive angles in a parallelogram are _________________________. C-29: The opposite angles in a parallelogram are _________________________. Example 1: Find the value of x in parallelogram ABCD. Then find mοA. Investigation: Determine which triangles are congruent. What do you notice about point T? βπ΅ππΆ ≅ β____________ by _________ βπ΄π΅π ≅ β____________ by _________ Μ Μ Μ Μ ≅ ______________ by _______________. Μ Μ Μ Μ ≅ ______________ and ππΆ So π΅π 8 So T is a ________________ of ___________ and ___________. C-30: The diagonals of a parallelogram _______________each other. Example 2: Find the values of x and y in parallelogram KLMN. 3 1 2 7 4 6 5 Check for Understanding: Summary Properties of Parallelograms ο· Opposite sides are ________________________. (Definition) ο· Opposite sides are ________________________. ο· Opposite angles are ________________________. ο· Consecutive angles are ________________________. ο· Diagonals ________________________ each other. Check for Understanding: Properties of Special Types of Quadrilaterals C-31: If three (or more) parallel lines cut off congruent segments on one transversal, then they cut off ___________ segments on every transversal. β‘ β₯ πΆπ· β‘ β₯ πΈπΉ Μ Μ Μ Μ ≅ πΆπΈ Μ Μ Μ Μ β‘ and π΄πΆ If: π΄π΅ Then: ________________________ Example 4: In the figure, β‘π·π» β₯ β‘πΆπΊ β₯ β‘π΅πΉ β₯ β‘π΄πΈ . Find EH.