Essay
Your teacher will grade your response to ensure that you receive proper credit for your answer.
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.'
(6 points)
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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 our knowledge of congruent triangles, let's examine the geometry of the baseball diamond.
First, we know that the distance from second base to first base is equal to the distance from second base to third base. This means that we have two congruent sides in both triangles formed by second base, first base, and home plate, as well as second base, third base, and home plate.
Now, let's look at the angles. The angle formed by first base, second base, and home plate is congruent to the angle formed by third base, second base, and home plate. Since both triangles share a congruent angle and two congruent sides, they must be congruent triangles.
In congruent triangles, all corresponding sides and angles are congruent. Therefore, if the distance from second base to first base is equal to the distance from second base to third base, and the angles formed by both bases and home plate are congruent, then the distance from first base to home plate must be equal to the distance from home plate to third base.
In conclusion, based on the congruent triangles formed by the angles and sides of the baseball diamond, we can conclude that the distance from first base to home plate is equal to the distance from home plate to third base.
To answer this question, we can use our knowledge of congruent triangles.
From the information given, we know that the distance from second base to first base is the same as the distance from second base to third base. Let's call this distance x.
Now, let's consider the angles formed. 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.
Since the angles are congruent, we can conclude that the triangles formed by home plate, first base, and second base are congruent to the triangles formed by home plate, third base, and second base.
Now, let's examine the congruent triangles. We can say that triangle A (formed by home plate, first base, and second base) is congruent to triangle B (formed by home plate, third base, and second base).
By definition of congruence, corresponding sides of congruent triangles are equal. Therefore, we can conclude that the distance from first base to home plate is equal to the distance from home plate to third base.
In other words, the distance from first base to home plate is x, and the distance from home plate to third base is also x.
Therefore, we can conclude that the distances from first base to home plate and from home plate to third base are equal.
To answer this question, we will use our knowledge of congruent triangles. Congruent triangles are triangles that have the same shape and size. When two triangles are congruent, we can conclude that their corresponding sides and angles are equal.
In this case, we have two congruent triangles to consider. First, we have the triangle formed by first base, second base, and home plate. Second, we have the triangle formed by third base, second base, and home plate.
Given the information that the distance from second base to first base is the same as the distance from second base to third base, we can conclude that these two triangles share a common side (the distance from second base to home plate). This means that the corresponding sides of these triangles are congruent.
Furthermore, we are told that the angles formed by first base, second base, and home plate have the same measure as the angles formed by third base, second base, and home plate. Since corresponding angles of congruent triangles are congruent, we can conclude that the angles in both triangles are congruent as well.
Based on this information, we can conclude that the distance from first base to home plate is equal to the distance from home plate to third base. In other words, the distance from first base to home plate is the same as the distance from home plate to third base.
Therefore, we can say that the distance from first base to home plate is equal to the distance from home plate to third base, based on our knowledge of congruent triangles.