![]() Enter your valid arguments, your answers, and work below. Prove that quadrilateral EFGH is or is not a rhombus. _ _ _ Part B Quinn wondered if quadrilateral EFGH is a rhombus. Part A Quinn thinks that quadrilateral EFGH is a parallelogram. Quinn then connected the midpoints to create quadrilateral EFGH. He located the coordinates of the midpoints of each side of the quadrilateral’s segments. He graphed quadrilateral ABCD on a set of coordinate axes such that A (-3, -2), B (-5,4), C (5,6), and D (1, -4). ITEM 209 Quinn is studying properties of quadrilaterals. These items may be used by Louisiana educators for educational purposes. Enter your proof that the 4 segment are equal in length and your work to determine that the non- consecutive segments are parallel below. _ _ _ Part B Determine that non-consecutive segments of the trail are parallel. Part A Prove that the 4 segments of the trail are equal in length. Use the information on the figure below to prove the landscape architect’s conjecture. The landscape architect conjectured that if she designs the trail in the shape of a rhombus that connects the midpoints of the adjacent sides, the trail will satisfy the Park Commission’s condition for the trail’s design. ITEM 208 The Parks Commission hired a landscape architect to design and construct a quadrilateral trail that connects the four sides of an isosceles trapezoid-shaped park, with all sides of the trail the same length. The constructed figure is equilateral triangle ABC not inscribed in a circle. The constructed figure is right scalene triangle ABC inscribed in a circle. The constructed figure is right isosceles triangle ABC not inscribed in a circle. The constructed figure is equilateral triangle ABC inscribed in a circle. Which of the following would be true for the constructed figure? A. Using a straightedge draw a line segment between point B and point C. Using a straightedge draw a line segment between point A and one of the intersection points of the two circles. ![]() Using a straightedge draw a line segment between the centers of the two circles. Create a circle with the center at point B such that circle B is congruent to circle A and circle B passes through point A. Create a circle with the center at point A 2. Congruence G-CO.D.13 Items 74 – 77 ITEM 74 The directions for a construction are shown below: 1. If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent. The sum of the squares of the lengths of the two shorter sides of a triangle is equal to the square of the length of the longest side of a triangle. If three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent. The sum of the measures of the interior angles of all triangles is 180°. Which postulate could Zhan be investigating using only these straw pieces and no other tools? A. The end of one piece is always touching the end of another piece. He moves the straw pieces to make triangles that have been translated, rotated, and reflected from an original position. Zhan cut a drinking straw into three pieces (shown above) to investigate a triangle postulate. Congruence G-CO.B.8 Item 37 ITEM 37 Use the diagram to answer the question. So together we will determine whether two triangles are congruent and begin to write two-column proofs using the ever famous CPCTC: Corresponding Parts of Congruent Triangles are Congruent.These items may be used by Louisiana educators for educational purposes. ![]() Knowing these four postulates, as Wyzant nicely states, and being able to apply them in the correct situations will help us tremendously throughout our study of geometry, especially with writing proofs. You must have at least one corresponding side, and you can’t spell anything offensive! We will explore both of these ideas within the video below, but it’s helpful to point out the common theme. Likewise, SSA, which spells a “bad word,” is also not an acceptable congruency postulate. Every single congruency postulate has at least one side length known!Īnd this means that AAA is not a congruency postulate for triangles. As you will quickly see, these postulates are easy enough to identify and use, and most importantly there is a pattern to all of our congruency postulates. ![]()
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