Chapter Closure
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Note that all transformations should be done with respect to the original triangle. Also, when you calculate the perimeter make sure you only take the shape's outermost sides into account.
24 feet
Notice that this is a right triangle with a hypotenuse and leg that are 5 and 3 feet, respectively. Therefore, this is a 3-4-5 triangle where the unknown leg is 4 feet.
Since we are reflecting △ ABC across AB, neither A or B will change positions. To reflect C, we have to make sure that BC and BC' have the same length and that CC' is perpendicular to the line of reflection.
Let's first mark the midpoint of BC.
Since we are rotating the triangle around the midpoint of BC by 180^(∘), the vertices of B and C will change positions. To rotate A, we have to use a protractor.
Let's draw the rotated triangle △ A'B'C'.
Since we are reflecting △ ABC across AC, only B will change position.
Let's draw the reflected triangle △ AB''C.
To calculate the perimeter of this new shape, we have to exclude any side lengths that are inside the shape.
Having identified the outermost sides of the new shape, we can determine its perimeter. Perimeter: 3+4+3+5+4+5=24 feet