Essay
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It is the same distance from second base to first base, and from second base to third base. The angle formed by first base, second base, and home plate has the same measure as the angle formed by third base, second base, and home plate. What can you conclude about the distance from first base to home plate, and from home plate to third base? Explain using your knowledge of congruent triangles.
The image of a baseball diamond is shown. The diamond itself is a square rotated so that a vertex is on the bottom. The bottom vertex is labeled 'Home,' the right vertex is labeled 'First,' the top vertex is labeled 'Second,' and the left vertex is labeled 'Third.' There is a diagonal drawn connecting 'Second' and 'Home.'
Based on the given information, we can conclude that the distance from first base to home plate is equal to the distance from home plate to third base.
To explain this using congruent triangles, we can observe that the triangle formed by first base, second base, and home plate is congruent to the triangle formed by third base, second base, and home plate.
First, let's consider the triangle formed by first base, second base, and home plate. Since it is given that the distance from second base to first base is equal to the distance from second base to third base, we can conclude that the sides opposite these angles are congruent. Let's label the distance from second base to first base as side A and the distance from second base to home plate as side B. Since A = B, we know that angle A is congruent to angle B.
Now, let's consider the triangle formed by third base, second base, and home plate. Since we know that angle A is congruent to angle B, we can conclude that the angle formed by third base, second base, and home plate (angle C) is also congruent to angle A and angle B.
Therefore, we can say that the two triangles are congruent by the Angle-Angle-Side (AAS) congruence theorem. And since the corresponding sides of congruent triangles are equal, we can conclude that the distance from first base to home plate is equal to the distance from home plate to third base.