Unit 10 Properties of Parallelograms
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1 Unit 10 Properties of Parallelograms Target 10.1: Use properties of parallelograms to solve problems 10.1a: Use Properties of Parallelograms 10.1b: Show that a Quadrilateral is a Parallelogram Target 10.2: Use properties of rhombuses, rectangles, and squares to solve problems Date Target Assignment Done! W a 10.1a Worksheet R b 10.1b Worksheet F 3-10 No School No School Teacher Institute M Worksheet T 3-14 Quiz Quiz W 3-15 Review Unit 10 Test Review R 3-16 Test Unit 10 Test Name:
2 10.1a Use Properties of Parallelograms Target 1: Use properties of parallelograms to solve problems Vocabulary: Parallelogram: Opposite Sides and Angles of a Parallelogram If a quadrilateral is a, then its and are congruent. Example 1: Use properties of parallelograms Find the values of x and y. What property did you use to find the value of x? How about y? Consecutive Interior Angles of a Parallelogram If a quadrilateral is a, then its are. Example 2: If KLMN is a parallelogram, find the values of x, y, and z.
3 Diagonals of a Parallelogram If a quadrilateral is a, then its. Example 3: Given that FGHJ is a parallelogram, find MH and FH. YOU TRY NOW! 1) Gates As shown, a gate contains several parallelograms. Find m ABC if m DAB = 65. 2) The diagonals of OLMN intersect at point P. Find the coordinates of P. You might need this midpoint = ( x 2+x 1 2, y 2+y 1 ) 2 YOUTRYNOW Answers: 1) 115 2)P(3.5, 2)
4 10.1b Show that a Quadrilateral is a Parallelogram Target 1: Use properties of parallelograms to solve problem Opposite Sides of a Parallelogram (CONVERSE) If both pairs of opposite sides of a quadrilateral are, then the quadrilateral is a. Opposite Angles of a Parallelogram (CONVERSE) If both pairs of opposite angles of a quadrilateral are, then the quadrilateral is a. Example 1: Use properties of parallelograms Basketball In the diagram, AB and DC represent an adjustable supports of a basketball hoop. Explain why AD is always parallel to BC. One Pair of Sides of a Parallelogram If one pair of are and, then the quadrilateral is a.
5 Bisected Diagonals of a Parallelogram If the diagonals of a bisect, then the quadrilateral is a. Example 2: Identify a parallelogram Lights The headlights of a car have the shape shown at the right. Explain how you know that B is congruent to D. Example 3: Use algebra with parallelograms For what value of x IS quadrilateral PQRS a parallelogram? What is the length of the diagonal PR? YOU TRY NOW! 1) What property can you use to show that the quadrilateral is a parallelogram? 2) What is the length of diagonal DG so that quadrilateral DFGH a parallelogram? YOUTRYNOW Answers: 1) The diagonals bisect each other. 2) 14
6 10.2 Properties of Rhombuses, Rectangles, and Squares Target 2: Use properties of rhombuses, rectangles and squares to solve problems Properties of Rhombuses, Rectangles and Squares Quadrilaterals Parallelograms What s the main difference between a rhombus and a rectangle? Rhombus Rectangle Squares Example 1: Use properties of parallelograms For any rhombus RSTV, decide whether the statement is always or sometimes true. a. S V b. T V Example 2: Classify special quadrilaterals Classify the special quadrilateral. Explain your reasoning.
7 Diagonals of a Rhombus A is a if and only if its are. A is a if and only if each are. Diagonals of a Rectangle A is a if and only if its are. Example 3: List properties of special parallelograms Sketch rectangle EFGH. List everything you know about it.
8 YOU TRY NOW! 1) You are building a frame for a painting. The measurements of the frame are shown at the right. a) The frame must be a rectangle. Given the measurements in the diagram, can you assume that it is? EXPLAIN! b) You measure the diagonals of the frame. The diagonals are about 25.6 inches. What can you conclude about the shape of the frame? 2) Sketch rhombus FGHJ. List everything you know about it. YOUTRYNOW Answers: 1)Answers may vary 2)Answers may vary
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