Question

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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.

Answer 1

The answer is

Converting this into a geometry problem requires us to name the points. Let give the home plate a symbol A, first base will be B, second base will be C, and the third base will be D. Now, we can present a geometrical proof:

STATEMENTS | REASONS

(1) BC = CD | Given

m(2) AC = AC | Reflexive Property

(3) triangle ACD = triangle ACB | SAS Congruence

(4) AD = AB | CPCTC

when CPCTC means Congruent Parts of Congruent Triangles are Congruent.

Therefore, the distance from first base to home plate, and from home plate to third plate are equal.Step-by-step explanation:

Answer 2

The answer is

Converting this into a geometry problem requires us to name the points. Let give the home plate a symbol A, first base will be B, second base will be C, and the third base will be D. Now, we can present a geometrical proof:

STATEMENTS | REASONS

(1) BC = CD | Given

m(2) AC = AC | Reflexive Property

(3) triangle ACD = triangle ACB | SAS Congruence

(4) AD = AB | CPCTC

when CPCTC means Congruent Parts of Congruent Triangles are Congruent.

Therefore, the distance from first base to home plate, and from home plate to third plate are equal.

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