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Download Section 6 - 2 Properties of Parallelograms.jnt
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GEOMETRY SECTION 6 – 2 PROPERTIES OF PARALLELOGRAMS Notes/Practice GOAL: To be able to identify the special properties of parallelograms and be able to use those properties in proof and in problem solving. PARALLELOGRAM: ____________________________________________________ ____________________________________________________________________ Quadrilaterals that are parallelograms: A. ___________________________ B. ___________________________ C. ___________________________ If MATH is a parallelogram, what conclusions can we make? Consecutive Angles: Angles of a polygon that _____________ a __________. In a parallelogram, consecutive angles are __________________________________. This means they add up to ____________. THIS IMPLIES THAT: ___________________________________________________ ____________________________________________________________________. GEOMETRY SECTION 6 – 2 PROPERTIES OF PARALLELOGRAMS Notes/Practice SOLVE for ALL variables given the following parallelogram. x = __________ y = __________ w = __________ z = __________ Now…we will use the definition of parallelograms, as well as properties we know from triangles, to prove some things about properties of parallelograms! I have started the first one for you, so you can see a new reason in proof! Proof 1: Given: MATH Prove: MA TH MH TA Statements 1. MATH 2. MA TH What did you just prove? Reasons 1. Given 2. 2 pairs of opposite sides GEOMETRY SECTION 6 – 2 PROPERTIES OF PARALLELOGRAMS Notes/Practice Proof 2: Given: MATH Prove: AW HW MW TW NOTE: What do we call AH and TM ? ______________________ Statements What did you just prove? Using what you just proved. Solve for x and y. Reasons GEOMETRY SECTION 6 – 2 PROPERTIES OF PARALLELOGRAMS Notes/Practice Last Theorem: Don’t need to prove it – If three (or more) parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal. If AB BC FE ED Uses of the above theorem…the first one is done for you!!! Find the value(s) of the unknowns. A. x = __________ B. x = __________ y = __________
