Question

wednesday, 10/1: write it out wednesday! here is a picture of an older version of the flag of great britain. there is a rigid transformation that takes triangle 1 to triangle 2, another that takes triangle 1 to triangle 3, and another that takes triangle 1 to triangle 4. a. what are the rigid transformations? b. triangle 1 has a side length of 5 inches, a bottom length of 8 inches, and a slanted side of 9.5 inches. how could you determine the side lengths of triangle 3 without measuring it? c. do all eight triangles in the flag have the same area?

Explanation:

Step1: Identify rigid - transformations

Rigid transformations preserve shape and size. Triangle 1 to Triangle 2 is a reflection (across a vertical line). Triangle 1 to Triangle 3 is a rotation (180 - degree rotation about the center of the flag). Triangle 1 to Triangle 4 is a reflection (across a horizontal line).

Step2: Use properties of rigid - transformations for side - lengths

Since rigid transformations preserve side - lengths, if Triangle 1 has side lengths 5 inches, 8 inches, and 9.5 inches, Triangle 3 (a 180 - degree rotation of Triangle 1) will have the same side lengths: 5 inches, 8 inches, and 9.5 inches.

Step3: Determine triangle areas

All eight triangles in the flag are congruent due to the rigid transformations. Congruent triangles have the same area. So, all eight triangles have the same area.

Answer:

A. Triangle 1 to Triangle 2: Reflection; Triangle 1 to Triangle 3: Rotation; Triangle 1 to Triangle 4: Reflection.
B. Since rigid transformations preserve side - lengths, Triangle 3 has side lengths 5 inches, 8 inches, and 9.5 inches.
C. Yes, all eight triangles have the same area because they are congruent due to rigid transformations.