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 Second ThirdFirst 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, let's consider triangle ABD and triangle CBD, where A, B, and D are the vertices of the bases (first base, second base, and home plate) and B is the vertex of the angle formed by the bases.
From the given information, we know that the distance from second base to first base (BD) is equal to the distance from second base to third base (BD). This means that side BD is congruent in both triangles ABD and CBD.
We also know that the angle formed by first base, second base, and home plate (angle ABD) has the same measure as the angle formed by third base, second base, and home plate (angle CBD). This means that angle ABD is congruent to angle CBD.
With congruent side BD and congruent angle ABD and CBD, by the Side-Angle-Side (SAS) congruence criterion, we can conclude that triangle ABD is congruent to triangle CBD.
Therefore, by the congruence of triangles ABD and CBD, we can say that side AD is congruent to side CD. In other words, the distance from first base to home plate is equal to the distance from home plate to third base.