Transformations and Congruence Unit Test
15 of 1515 of 15 Items
Question
Use the image to answer the question.
An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 10 to 10 in increments of 1. Two triangles, upper A upper B upper C and upper E upper G upper H, are plotted on the graph. The triangle upper A upper B upper C has its vertices marked with closed points at upper A left parenthesis 1 comma negative 3 right parenthesis, upper B left parenthesis 1 comma negative 1 right parenthesis, and upper C left parenthesis 4 comma negative 3 right parenthesis. The triangle upper E upper G upper H has its vertices marked with closed points at upper E left parenthesis negative 2 comma 5 right parenthesis, upper G left parenthesis negative 2 comma 2 right parenthesis, and upper H left parenthesis negative 4 comma 2 right parenthesis. In triangle upper E upper G upper H, side upper E upper G is labeled as h, side upper G upper H is labeled as e, and side upper H upper E is labeled as g.
△ABC is congruent to △GHE . Describe a sequence of transformations from △ABC to △GHE that proves their congruence.
One possible sequence of transformations would be:
1. Translation: Shift △ABC 3 units to the left and 6 units up to coincide with △GHE. This would show that the corresponding vertices of the triangles match after the translation.
2. Rotation: Rotate △ABC clockwise 180 degrees around the point of intersection of the x and y axes. This would show that the angles of the triangles match after the rotation.
3. Reflection: Reflect △ABC over the y-axis. This would show that the sides of the triangles match after the reflection.
By performing these transformations in sequence, it can be demonstrated that △ABC is congruent to △GHE.