Parallelogram - Berkeley City College

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H K E N R V F C M Q D A L T P B G J Statements Reasons 1. AB||CD||EF , LM ∼ = NM 1. Given 2. Construct V T through Q parallel to LN 2. Parallel Postulate 3. NMQV and MLT Q are parallelograms 3. Def. of <strong>Parallelogram</strong>s 4. MN ∼ = QV , LM ∼ = T Q 4. Opposite sides of are ∼ = 5. V Q ∼ = T Q 5. Substitution 6. ∠RV Q ∼ = ∠P T Q, ∠V RQ ∼ = ∠T P Q 6. Alternate Interior Angles 7. △RV Q ∼ = △P T Q 7. AAS 8. RQ ∼ = P Q 8. CPCTC Theorem: If a line is drawn from the midpoint of one side of a triangle and parallel to a second side, then that line bisects the third side. In picture below, M is the midpoint of AB. If we construct a line through M parallel to AC, then this line will intersect BC at N, where N is the midpoint of BC B M N A C The converse of this theorem is also true. If a line connects the midpoints of two sides of a triangle, then the line is parallel to the third side. In addition, the length of this line is half of the length of the third side. In the picture above, if M is the midpoint of AB and N is the midpoint of CB, then MN||AC, and MN = 1 2 AC Theorem: The three medians of a triangle intersect at a point (the centroid of the triangle). This point is two-thirds of the distance from any vertex to the
midpoint of the opposite side. B E F M A D C In the above, if AF , CE, and BD are medians of △ABC, then they intersect at a single point, M, and CM = 2ME, AM = 2MF , BM = 2MD.
Page 1 and 2: Definition: A quadrilateral is a po
Page 3 and 4: Theorem: Opposite angles of a paral
Page 5: Properties Parallelogram Rectangle

Parallelogram - Berkeley City College

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