Question

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josh runs from the northwest corner to the southeast corner of a rugby field, and mia runs from the northeast corner to the southwest corner. mia says she ran farther. is she correct? explain. choose the correct answer below. a. yes. the path that mia ran created a triangle with a hypotenuse that is longer than the hypotenuse of the triangle created by the path that josh ran. thus, mia ran farther. b. yes. the path that mia ran created a triangle with a base that is longer than the base of the triangle created by the path that josh ran. thus, mia ran farther. c. no. the path that mia ran created a triangle with a base that is shorter than the base of the triangle created by the path that josh ran. thus, josh ran farther. d. no. the paths they ran created two triangles, which can be shown to be congruent by sas. thus, by cpctc they both ran the same distance.

Explanation:

Step1: Consider the field as a rectangle

The paths of Josh and Mia are diagonals of the rectangle - shaped rugby field.

Step2: Recall rectangle properties

In a rectangle, the diagonals are of equal length. The triangles formed by their paths can be shown to be congruent by Side - Angle - Side (SAS) congruence criterion (sides of the rectangle are equal and the included right - angles are equal). Then by Corresponding Parts of Congruent Triangles are Congruent (CPCTC), the lengths of their paths are equal.

Answer:

D. No. The paths they ran created two triangles, which can be shown to be congruent by SAS. Thus by CPCTC they both ran the same distance.