Question

1. write two true statements about the angles shown below: b a 45° c 6) describe a unique shape? 7) write two true statements about rigid transformations and congruency. 8) if angle bad is 80°, what is the measure of angle f true or false:

Explanation:

Step1: Analyze vertical - angles for question 5

Vertical angles are equal. Angle $a$ and the $45^{\circ}$ angle are vertical angles, so $a = 45^{\circ}$. Also, $b$ and $c$ are vertical angles, so $b=c$.

Step2: Define a unique shape for question 6

A regular dodecahedron is a unique shape. It is a three - dimensional polyhedron with 12 regular pentagonal faces, 30 edges, and 20 vertices.

Step3: State facts about rigid transformations and congruency for question 7

1. Rigid transformations (translations, rotations, reflections) preserve the size and shape of a figure. So, if figure $A$ is obtained from figure $B$ by a rigid transformation, then figure $A$ and figure $B$ are congruent.
2. Two congruent figures can be mapped onto each other by a sequence of rigid transformations.

Answer:

1. Statement 1: $a = 45^{\circ}$; Statement 2: $b = c$
2. A regular dodecahedron is a three - dimensional polyhedron with 12 regular pentagonal faces, 30 edges, and 20 vertices.
3. Statement 1: Rigid transformations preserve the size and shape of a figure, so figures related by rigid transformations are congruent. Statement 2: Congruent figures can be mapped onto each other by rigid transformations.