- #1
Bashyboy
- 1,421
- 5
Hello,
Suppose that I have two triangles ##\bigtriangleup ABC## and ##\bigtriangleup XYZ## that are known to be congruent by the side-side-side axiom, from which it follows that the parts are also congruent, such as the angles. My question is, how do I determine which of the three angles of ##\bigtriangleup ABC## is congruent to ∠ A, for example? Visually, it is clear that ##\angle A \cong X##, but I am having difficulty justifying this? Do I perform isometries until the vertices align, and then I can infer precisely which angles of ##\bigtriangleup ABC## are congruent to ##\bigtriangleup ABC##?
Suppose that I have two triangles ##\bigtriangleup ABC## and ##\bigtriangleup XYZ## that are known to be congruent by the side-side-side axiom, from which it follows that the parts are also congruent, such as the angles. My question is, how do I determine which of the three angles of ##\bigtriangleup ABC## is congruent to ∠ A, for example? Visually, it is clear that ##\angle A \cong X##, but I am having difficulty justifying this? Do I perform isometries until the vertices align, and then I can infer precisely which angles of ##\bigtriangleup ABC## are congruent to ##\bigtriangleup ABC##?