WORKBOOK SAMPLER Chapter 7: Polygons - Nelson Education

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Hint Use diagrams from Example 1 to help you with Question 3. Practice 1. Which convex quadrilaterals have each property a) two pairs of equal sides: and rhombus b) four right angles: c) equal diagonals: d) equal angles at opposite vertices: parallelogram, and rhombus 2. How can you use properties to show that a rectangle is a parallelogram A rectangle is a parallelogram because it has 3. The diagonals in a square are perpendicular. The diagonals cross at their midpoints. Record the names of other types of quadrilaterals to complete the chart. Property Diagonals are perpendicular. Diagonals cross at their midpoints. rectangle, square, parallelogram, rectangle and square rectangle and square opposite sides that are parallel and equal A quadrilateral with this property e.g., kite e.g., rhombus rectangle, square, A quadrilateral without this property e.g., parallelogram e.g., kite . Hint Draw some quadrilaterals. Measure the exterior angles to test your answer for Question 4. 4. a) Show that the exterior angles of all quadrilaterals have the same sum. • At each vertex, the measure of the interior angle plus the measure of the exterior angle equals 1808 . • There are four vertices. The total sum of all the interior and exterior angles of a quadrilateral is 4 ( 1808 ) 5 7208 . • The sum of the interior angles is 3608 . • The sum of the exterior angles is 7208 2 3608 5 3608 . • The sum of the exterior angles of any quadrilateral is 3608 . b) Do all quadrilaterals have diagonals that are perpendicular Explain. No. e.g., The parallelogram, trapezoid, and irregular quadrilateral in Example 1 do not have diagonals that are perpendicular. 170 Apprenticeship and Workplace 12 NEL 14 Apprenticeship and Workplace 12 NEL
5. Jay makes picture frames. The interior angles of the square picture frame have a sum of 3608. How can you draw a diagonal to show that all quadrilaterals have this property e.g., I looked at one diagonal in each quadrilateral in Example 1. You get two triangles. The sum of the interior angles of each triangle is 1808. The sum of the interior angles of both triangles is 2(1808) 5 3608. 6. An isosceles trapezoid is cut from an isosceles triangle. It has two equal sides and two parallel sides. The parallel sides are called bases. a) Use the isosceles triangle at the right. Draw a line parallel to the base to make an isosceles triangle. Measure to check that there are two equal side lengths in the trapezoid. b) What are two properties of your isosceles trapezoid e.g., one pair of equal sides and two pairs of equal angles OR equal diagonals c) Compare your isosceles trapezoid with isosceles trapezoids drawn by your classmates. What is one property that is shared by all the isosceles trapezoids AW12SB 0176519637 e.g., one pair of equal sides OR two pairs of congruent FN CO Technical Pass Approved Not Approved C07-F40-AW12SB angles OR two different angles that add to 1808 OR two CrowleArt Group isosceles triangles and two congruent triangles that are formed where the diagonals meet 2nd pass 7. When you join the midpoints of all four sides of a quadrilateral, you always get the same type of polygon. Test some quadrilaterals. What is the polygon parallelogram 4(90°) 360° Hint Think about • side lengths • angle measures • diagonals 7. e.g., 8. Darcy is cutting glass for a window that is a rhombus. She knows that the sides are 10 in. long. Does she have all the information she needs to cut the glass Explain. Include a diagram. No. e.g., She also needs to know the angle measures. There are many rhombuses such as a square with the same side lengths. 8. e.g., 10 in. 10 in. NEL NEL Chapter 7 Polygons 173 Chapter 7 Polygons 15
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WORKBOOK SAMPLER Chapter 7: Polygons - Nelson Education

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