Question

AB BG, AC GC, ZABC LGBC ZBACZBGC

A
B
#
C
G
1. What rigid transformation will take triangle GBC onto triangle ABC?

2. Explain why G' will coincide with A

3. Is triangle GBC congruent to triangle ABC? Explain your reasoning, and be sure to list any sides/angles you compared.

CAN SOMEONE HELP ME PLS, YOU’LL EARN FREE EASY POINTS IF IT’S THE RIGHT ANSWER, NO RANDOM ANSWERS BC YA’LL BE GIVING ME THE WRONG ANSWER SOMETIMES :(

Answer 1

Triangle GBC can be taken onto triangle ABC using a translation. G' will coincide with A. Triangle GBC is congruent to triangle ABC.

Step-by-step explanation:

The given information states that AB is congruent to BG and AC is congruent to GC. It also states that ZABC is congruent to LGBC and ZBACZBGC. Based on this information, we can conclude that triangle GBC can be taken onto triangle ABC using a translation, or a rigid transformation that slides the figure without changing its size or shape.

To explain why G' will coincide with A, we can observe that A is the only common point between both triangles. Since triangle GBC can be taken onto triangle ABC using translation, the translation would move G' onto A, resulting in them coinciding.

Triangle GBC is congruent to triangle ABC because they can be transformed onto each other using a rigid transformation. Specifically, a translation can take triangle GBC onto triangle ABC, which preserves the size and shape of the triangles.

Answer 2

Step-by-step explanation:

1) Reflection over
`\overline{BC}`

2) The triangles are congruent by SAS, so when
`\triangle GBC` is mapped onto
`\triangle ABC`, because points
`G` and
`A` are corresponding,
`G'` will correspond with
`A`.

3) Yes, because
`\overline{BG} \cong \overline{AB}, \overline{GC} \cong \overline{AC}, \angle BAC \cong \angle BGC`, so the triangles are congruent by SAS.