7.G.B.5 – Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
HSG.GPE.B.6 – Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
HSG.GPE.B.7 – Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
G.2(A) – determine the coordinates of a point that is a given fractional distance less than one from one end of a line segment to the other in one- and two-dimensional coordinate systems, including finding the midpoint
G.2(B) – derive and use the distance, slope, and midpoint formulas to verify geometric relationships, including congruence of segments and parallelism or perpendicularity of pairs of lines
G.6(A) – verify theorems about angles formed by the intersection of lines and line segments, including vertical angles, and angles formed by parallel lines cut by a transversal and prove equidistance between the endpoints of a segment and points on its perpendicular bisector and apply these relationships to solve problems