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6.6. Special Quadrilaterals. SUMMARIZING PROPERTIES OF QUADRILATERALS. 1. GOAL. EXAMPLE 1. By now you should now the distinguishing properties of each of the seven types of quadrilaterals we have studied. DO YOU???. EXAMPLE 2. Extra Example 1.
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6.6 Special Quadrilaterals SUMMARIZING PROPERTIES OF QUADRILATERALS 1 GOAL EXAMPLE 1 By now you should now the distinguishing properties of each of the seven types of quadrilaterals we have studied. DO YOU???
EXAMPLE 2 Extra Example 1 ABCD has at least two congruent consecutive sides. What quadrilaterals meet this condition? Hint: There are three. rhombus, square, kite
F A B G E D C H Extra Example 2 When you join the midpoints of the sides of an isosceles trapezoid in order, what special quadrilateral is formed? Why?
6.6 Special Quadrilaterals PROOF WITH SPECIAL QUADRILATERALS 2 GOAL EXAMPLE 3 You should know the different methods used to show a quadrilateral is a specific shape. You will use either the definition of the shape or one of the theorems. This is explained in the concept summary found on page 365. Note: These are specific for rhombuses!
Extra Example 3 The coordinates of ABCD are A(–2, 5), B(1, 8), C(4, 5), and D(1, 2). What are at least two ways to show that ABCD is a rhombus?
EXAMPLE 4 Checkpoint The diagonals of RSTQ are perpendicular. What quadrilaterals meet this condition? square, rhombus, kite
EXAMPLE 5 Extra Example 4
The diagonals of ABCD intersect at point N to form four congruent isosceles triangles: What type of quadrilateral is ABCD? Extra Example 5
Checkpoint The diagonals of ABCD are congruent. and What kind of figure is ABCD ? isosceles trapezoid
QUESTION: At least two opposite angles of EFGH are congruent. What kind of quadrilateral might it be? ANSWER: parallelogram, rhombus, rectangle, square, kite