Evidence of Understanding

**describe the relationship between angles formed by two intersecting lines**- use tools to explore and describe linear pairs and vertical angles
- Discuss the impacts of human error

- justify, using transformations and constructions, that vertical angles are congruent
- use the angle addition postulate to show why
**supplementary angles**sum to 180 - deductively prove vertical angles must be congruent using the
**reflexive**and**transitive properties**- explain and apply the subtraction property of equality (Euclid’s third common notion)

- find the measure of an angle using
**complementary**, supplementary, or vertical pairs

- use tools to explore and describe linear pairs and vertical angles
**explore angle relationships formed by a transversal and a pair of parallel lines**- use tools to make conjectures about
**parallel**lines with a**transversal**- use constructions and transformations (and other tools) to map angles to each other
- construct two congruent angles using a rigid motion transformation and parallel lines
- measuring many pairs of angles and generalizing findings to justify when two angles are congruent or supplementary

- prove that two lines are parallel using congruent angle relationships (the converse statement)
- apply properties of vertical angles and linear pairs to prove that two angles are congruent or supplementary
- create shared definitions for
**corresponding**,**alternate interior**,**alternate exterior, same-side interior or same-side exterior angles**(also referred to as**consecutive interior**or**consecutive exterior**angles) - find the measure of a missing angle

- use tools to make conjectures about

Develop conceptual understanding:

linear pair, supplementary, vertical angles, reflexive property, transitive property, complementary, parallel, transversal, corresponding, alternate interior, alternate exterior, same-side (or consecutive) interior angles, same-side (or consecutive) exterior anglesSupporting terms to communicate:

adjacent, opposite, perpendicular, bisect, degree measure, human error, sum, equal measure, congruent, construct, rotate, translate, reflect, map, carry onto