Question

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 the third base to home plate,and from home plate to third base? Explain using your knowledge of congruent triangles

Answer 1

a 90 degree angle is formed

Answer 2

Distance between first base to home plate and from home plate to third plate are equal.

Explanation:

Given : 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 the third base to home plate,and from home plate to third base.

To explain : The given situation and distance between first base to home plate and from home plate to third plate are equal.

Solution : Converting the given situation into a geometry problem. So we name the require points.

Let A be the home plate,

B is first base,

C is the second base,

And D is the third base.

Now, we can present a geometrical proof:

Statement and their reasons

(1) BC = CD - ( Given )

(2) AC = AC - ( Reflexive Property )

(3) Δ ACD = Δ ACB - ( SAS Congruence - side angle side)

(4) AD = AB - ( CPCTC - Congruent Parts of Congruent Triangles are Congruent )

Therefore, the gap from 1st base to home plate, and from home plate to 3rd plate are equal.