Common Core State
HSG.SRT.A3
Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
October 1, 2018HSG.SRT.B4
Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
October 1, 2018HSG.SRT.B5
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
October 1, 2018HSG.SRT.C6
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
October 1, 2018HSG.SRT.C7
Explain and use the relationship between the sine and cosine of complementary angles.
October 1, 2018HSG.SRT.C8
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.*
October 1, 2018HSG.GPE.B5
Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
October 1, 2018HSG.GPE.B6
Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
October 1, 2018HSG.GPE.B7
Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.*
October 1, 2018HSG.CO.C9
Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.
October 1, 2018HSG.CO.C10
Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
October 1, 2018HSG.CO.C11
Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.
October 1, 2018