![]() ![]() Join the rest of the straws to form a quadrilateral with opposite sides congruent. Partly unbend two paperclips, link their smaller ends, and insert the larger ends into two cut straws. Investigating Properties of Parallelograms Cut 4 straws to form two congruent pairs. ![]() Geometry 1 Unit 6 6.3 Proving Quadrilaterals are Parallelogramsģ0 Proving Quadrilaterals are Parallelograms Is the slab a parallelogram? Explain.Ģ9 6.3 Proving Quadrilaterals are Parallelograms Prove: ∆BCD ∆EFA A B C F D EĮxample 6 A four-sided concrete slab has consecutive angle measures of 85°, 94°, 85°, and 96°. Opposite sides of a parallelogram are congruent AC = DF AB = DE AC = AB + BC DF = DE + EF AC = DE + DF AB + BC = AB + EF BC = EF Def of Congruent ∆BCD ∆EFA Example 5 Given: ACDF is a parallelogram. Statement Reason ACDF is a parallelogram. Statement Reasons ABCD is a parallelogram AD || BC 2 1 AB || CD Alternate interior angles theorem 2 4 Example 4 Given: ABCD is a parallelogram. mA mDĮxample 3 WXYZ is a parallelogram. Find each unknown length JH LH G K H J L 6 8 JH = 8 LH = 6Įxample 2 In ABCD, mC = 105°. P Q S R M QM SM and PM RMĮxample 1 GHJK is a parallelogram. P Q S R P R and Q SĬonsecutive Angles in a Parallelogram Theorem If a quadrilateral is a parallelogram, then its consecutive angles are supplementary R Add to equal 180° Q mP + mQ = 180° mQ + mR = 180° mR + mS = 180° mS + mP = 180° S Pĭiagonals in a Parallelogram Theorem If a quadrilateral is a parallelogram, then its diagonals bisect each other. Opposite Angles in a Parallelogram Theorem If a quadrilateral is a parallelogram, then its opposite angles are congruent. Opposite Sides of a Parallelogram Theorem If a quadrilateral is a parallelogram, then its opposite sides are congruent. Quadrilateral with two pairs of parallel sides. ![]() Geometry 1 Unit 6 6.2 Properties of Parallelograms x 55° E H F Gġ6 Polygons Example 4 Use the information in the diagram to solve for x The sum of the measures of the interior angles of a quadrilateral is 360°. Polygons with no diagonals on the outside of the polygonĪ polygon is concave if at least one diagonal is outside the polygon These are also called nonconvex.ġ0 Polygons Example 1 Identify the polygon and state whether it is convex or concave.ġ1 Polygons Equilateral Polygon Equiangular Polygon Regular PolygonĪll sides the same length Equiangular Polygon all angles equal measure Regular Polygon equilateral and equiangularġ2 Polygons Equilateral Equiangular Regularġ3 Polygons Example 2 Decide whether the polygon is regular.ġ4 Polygons Interior Angles of a Quadrilateral Theorem 3 Polygons Polygon Sides Vertex A closed figure in a planeįormed by connecting line segments endpoint to endpoint Each segment intersects exactly 2 others Classified by the number of sides they have Named by listing vertices in consecutive order Sides Line segments in a polygon Vertex Each endpoint in a polygonĥ Polygons Pentagon ABCDE or pentagon CDEAB A D C B EĦ Polygons Sides Name 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagonħ Heptagon 8 Octagon 9 Nonagon 10 Decagon 11 Undecagon 12 Dodecagon n n-gon (a 19 sided polygon is a 19-gon)ħ Polygons Diagonals Line segments that connect non-consecutive vertices.
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