Question
Use the image to answer the question.
An illustration shows two quadrilaterals. Quadrilateral A C B D is smaller than quadrilateral G H F E. In quadrilateral A C B D, angle A measures 90 degrees, angle C measures 108 degrees, angle B measures 90 degrees, and angle D measures 72 degrees. In quadrilateral G H F E, angle G measures 90 degrees, angle H measures 108 degrees, angle F measures 90 degrees, and angle E measures 72 degrees.
Which statement correctly describes the similarity between the two quadrilaterals?
An illustration shows two quadrilaterals. Quadrilateral A C B D is smaller than quadrilateral G H F E. In quadrilateral A C B D, angle A measures 90 degrees, angle C measures 108 degrees, angle B measures 90 degrees, and angle D measures 72 degrees. In quadrilateral G H F E, angle G measures 90 degrees, angle H measures 108 degrees, angle F measures 90 degrees, and angle E measures 72 degrees.
Which statement correctly describes the similarity between the two quadrilaterals?
Answers
Answered by
GPT-4o mini
The two quadrilaterals, ACBDA and GHFE, are similar because they have corresponding angles that are equal. Specifically, both quadrilaterals exhibit the following angles:
- Angle A (90 degrees) corresponds to angle G (90 degrees).
- Angle C (108 degrees) corresponds to angle H (108 degrees).
- Angle B (90 degrees) corresponds to angle F (90 degrees).
- Angle D (72 degrees) corresponds to angle E (72 degrees).
Since all corresponding angles are equal, the quadrilaterals ACBDA and GHFE are similar by the Angle-Angle (AA) criterion for similarity of polygons. Additionally, since they are both quadrilaterals with equal corresponding angle measures, they maintain the same shape but differ in size. Thus, we can conclude that quadrilateral ACBDA is similar to quadrilateral GHFE.
- Angle A (90 degrees) corresponds to angle G (90 degrees).
- Angle C (108 degrees) corresponds to angle H (108 degrees).
- Angle B (90 degrees) corresponds to angle F (90 degrees).
- Angle D (72 degrees) corresponds to angle E (72 degrees).
Since all corresponding angles are equal, the quadrilaterals ACBDA and GHFE are similar by the Angle-Angle (AA) criterion for similarity of polygons. Additionally, since they are both quadrilaterals with equal corresponding angle measures, they maintain the same shape but differ in size. Thus, we can conclude that quadrilateral ACBDA is similar to quadrilateral GHFE.