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Transcript
January 27, 2017 Unit 7 Lesson 6 Special Parallelograms, part 1 "There is no royal road to geometry." - Euclid (said in response to King Ptolemy's plea for an easier way to learn mathematics.) Rhombus -a quadrilateral with four equal sides (equilateral) Why is every rhombus a parallelogram? January 27, 2017 1. Go to my website (www.tinyurl.com/WrightGeometry) 2. Scroll down and select the Rhombus link next to Unit 7, Lesson 6 3. Answer the following questions. a) Are the diagonals always congruent?_________ b) Do the diagonals always bisect the angles?___________ c) Are the diagonals always perpendicular?____________ Consider the rhombus below. What can we say about the 4 triangles formed by the when the diagonals are drawn? Why? January 27, 2017 Rhombus Recap: 1. a quadrilateral with four congruent sides (definition) 2. Diagonals are perpendicular (theorem 5-13) 3. Diagonals bisect the angles (theorem 5-14) Rectangle - a quadrilateral with four right angles. (equiangular) Why is every rectangle a parallelogram? January 27, 2017 1. Go to my website (www.tinyurl.com/WrightGeometry) 2. Scroll down and select the Rectangle Link next to Unit 7, Lesson 6 3. Answer the following questions. a) Are the diagonals always congruent?_________ b) Do the diagonals always bisect the angles?___________ c) Are the diagonals always perpendicular?____________ Consider the rectangle below. Explain why . What does this ultimately mean about a rectangle? January 27, 2017 January 27, 2017 Rectangle Recap: 1. a quadrilateral with four right angles (or four congruent angles) (definition) 2. Diagonals are congruent. (theorem 5-12) Extension: Theorem 5-15 The midpoint of the hypotenuse of a right triangle is equidistant from the three vertices. Example 1: Find the value of x in rectangle ABCD January 27, 2017 Example 2: Find the value of x and y in rhombus ABCD. 10 6 y Example 3: If the diagonals of a quadrilateral are perpendicular, must it be a rhombus? Explain. If the diagonals of a quadrilateral are congruent, must it be a rectangle? Explain.
