QuestionIs this shape a square? Choose the correct reason: A. Perpendicular sides, equal length. B. Parallel sides, equal length. C. Opposite sides not parallel. D. Sides not congruent.
Studdy Solution
STEP 1
Assumptions1. The shape in question has four sides. . The properties of the shape are as stated in the options A, B, C, and D.
STEP 2
We need to understand the properties of a square to answer this question. A square is a quadrilateral with the following properties1. All sides are of equal length (congruent).
2. Each angle is a right angle (90 degrees).
. The opposite sides are parallel.
STEP 3
Now, let's evaluate each option against these properties.
Option A Yes, the adjacent sides are perpendicular, and all sides are the same length.This statement is true for a square. All adjacent sides of a square are perpendicular (forming a right angle), and all sides are of the same length.
STEP 4
Option B Yes, the opposite sides are parallel, and all sides are the same length.
This statement is also true for a square. All opposite sides of a square are parallel, and all sides are of the same length.
STEP 5
Option C No, the opposite sides are not parallel.
This statement indicates that the shape is not a square. As we established in Step2, one of the properties of a square is that its opposite sides are parallel.
STEP 6
Option D No, the sides are not congruent.
This statement also indicates that the shape is not a square. As we established in Step2, another property of a square is that all its sides are of equal length (congruent).
STEP 7
From the above analysis, we can conclude that the shape is a square if the properties stated in options A or B are true. If the properties stated in options C or D are true, then the shape is not a square.
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