16 Cirele the quadrilateral with diagonals congruent, perpendicular to each othe

Question

16 Cirele the quadrilateral with diagonals congruent, perpendicular to each other and bisecting each other. (B) rectangle (C) square (D) regular polygon carpenter must ensure that a large window frame is a rectangle. If the coners are labeled A, B, C, and D. the carpenter knows that AB = 51 inches, BC-68 inches, CD = 51 inches. and AD 68 inches. The carpenter used a string to verify that the diagonals AC and BD are the sa out iame length, and so insists that ABCD must be a true rectangle. Finish the reasoning outlined below to justify the carpenter's logic. ACO ABCD is a rectangle since n . ify the quadrilateral shown on the right and explain your reasoning. 6f . The quadrilateral is a A(2509)-04/12-08 AMERICAN SCHOOL Lansing, II

Explanation / Answer

16)

The rhombus has the following properties:

17) since the opposite sides were equal and the interior was 90 each that shows that the quadrilateral was a rectangle.

18) The quadrilateral shown is a rhombus beacause :

All the properties of a parallelogram apply (the ones that matter here are parallel sides, opposite angles are congruent, and consecutive angles are supplementary).

All sides are congruent by definition.

The diagonals bisect the angles.

The diagonals are perpendicular bisectors of each other.

The rhombus has the following properties:

All the properties of a parallelogram apply (the ones that matter here are parallel sides, opposite angles are congruent, and consecutive angles are supplementary).

All sides are congruent by definition.

The diagonals bisect the angles.

The diagonals are perpendicular bisectors of each other.

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