Question

Given points A(0, 0), B(4, 0), C(0, 2), D(0, 0), E(12, 0) and F(0, 6), prove that triangle ABC triangle DEF.

Answer 1

To prove triangle ABC congruent to triangle DEF, we can find the lengths of their corresponding sides and show they are equal.

1. Given points A(0, 0), B(4, 0), C(0, 2), D(0, 0), E(12, 0), and F(0, 6).
2. We can find the lengths of the sides of both triangles to show congruence.
3. The length of AB is 4 units, BC is 2 units, and AC is the hypotenuse of a right triangle with legs 2 and 4 (by using the distance formula), which is equal to √20.
4. The length of DE is 12 units, EF is 6 units, and DF is the hypotenuse of a right triangle with legs 6 and 12, which is also equal to √20.
5. Since all corresponding sides of both triangles have the same lengths, triangle ABC is congruent to triangle DEF by the Side-Side-Side (SSS) congruence criterion.

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