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4.1 Properties of a Parallelogram

4.1 Properties of a Parallelogram. Parallelogram is a quadrilateral in which both pairs of opposite sides are parallel. Theorem 4.1.1: A diagonal of a parallelogram separates it into two congruent triangles. Proof p. 178* Strategy p. 179. Parallelogram Relationships.

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4.1 Properties of a Parallelogram

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  1. 4.1 Properties of a Parallelogram • Parallelogram is a quadrilateral in which both pairs of opposite sides are parallel. • Theorem 4.1.1: A diagonal of a parallelogram separates it into two congruent triangles. Proof p. 178* Strategy p. 179 Section 4.1 Nack

  2. Parallelogram Relationships • Corollary 4.1.2: The opposite angles of a parallelogram are congruent. • Corollary 4.1.3: The opposite sides of a parallelogram are congruent. • Corollary 4.1.4: The diagonals of a parallelogram bisect each other • Corollary 4.1.5: Two consecutive angles of a parallelogram are supplementary. Ex. 2 p. 179 Section 4.1 Nack

  3. Additional Theorems • Theorem 4.1.6: Two parallel lines are everywhere equidistant. Ex. 3 p. 181 • Altitude of a parallelogram is a line segment from one vertex that is perpendicular to a nonadjacent side (or to an extension of that side). Section 4.1 Nack

  4. Lemma 4.1.7: If two sides of one triangle are congruent to two sides of a second triangle and the included angle of the first triangle is greater than the included angle of the second, then the length of the side opposite the included angle of the first triangle is greater than the length of the side opposite the included angle of the second. In this diagram, AC > DF A D B C E F • Theorem 4.1.8: In a parallelogram with unequal pairs of consecutive angles, the longer diagonal lies opposite the obtuse angle. Ex. 6 p. 182 Section 4.1 Nack

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