Evidence of Understanding

**describe qualities that make two angles congruent or incongruent**- define an
**angle**using its**vertex**and**rays**- recognize that as an angle measure increases, its arc measure increases

- define all straight angles as having 180° and are therefore all congruent angle measures
- show and describe why an angle whose arc measure is 180° is also a semi-circle
- show and describe why an angle whose arc measure is 360° is also a complete circle

- justify which qualities are mathematically significant or insignificant for determining if two angles are the same
*Example:***degree measure**vs. color of the angle, length of the rays, thickness, etc.

- define an
**construct congruent angles and justify their congruence**- compare methods for determining congruence and describe advantages of each type
*Examples: paper folding, placing angles on the coordinate grid, using patty paper or online software to translate, rotate, or reflect image, etc.*

- given an angle, create a congruent angle, and explain why they are congruent
- use notation to signify congruence
- consider and describe implications of human error

- bisect an angle and justify congruence of both parts
- use
**angle addition**to explain that each part is half the degree measure of the whole - construct congruent
**right angles**using a**perpendicular bisector**

- use

- compare methods for determining congruence and describe advantages of each type
**perform constructions and analyze the relationships among the segments or angles created**- explore congruent relationships between segments and angles formed by constructing a perpendicular bisector
- describe how two congruent angles are
**sectors**of the same circle, including congruent radii and arc measures

Develop conceptual understanding:

angle, vertex, ray, degree measure, sector of a circle, perpendicular, angle addition, right angle, perpendicular, perpendicular bisector, straight angleSupporting terms to communicate:

congruent, incongruent, point, line, line segment, length measure, acute, obtuse, circle, arc, radius, equidistant, distance, bisect, midpoint, compass, construction, partition, protractor