Geometry (Ohio's Learning Standards)

Congruence (G.CO)

• G.CO.1 Know precise definitions of angle, circle, perpendicular and parallel lines and segment from undefined notions.
• G.CO.2 Represent transformations as functions of points and compare rigid motions with other transformations.
• G.CO.3 Identify the symmetries of a figure (rotations and reflections that map it onto itself).
  • a. Identify line-symmetric figures and use lines of symmetry to analyze them.
  • b. Identify rotational symmetry, find the angles and analyze properties.
• G.CO.4 Develop definitions of rotations, reflections and translations using angles, circles, lines and segments.
• G.CO.5 Draw transformed figures with tools or software and give a sequence mapping one figure onto another.
• G.CO.6 Use rigid motions to transform figures, predict their effect and decide congruence.
• G.CO.7 Show triangles are congruent exactly when corresponding sides and angles are congruent.
• G.CO.8 Explain how ASA, SAS and SSS follow from congruence defined by rigid motions.
• G.CO.9 Prove and apply theorems about lines and angles, such as vertical angles, transversals and perpendicular bisectors.
• G.CO.10 Prove and apply triangle theorems: angle sum, isosceles base angles, midsegment, medians meet at a point.
• G.CO.11 Prove and apply parallelogram theorems about sides, angles and diagonals, including rectangle diagonals.
• G.CO.12 Make formal constructions with compass and straightedge, paper folding or dynamic software.
• G.CO.13 Construct an equilateral triangle, a square and a regular hexagon inscribed in a circle.
• G.CO.14 Classify 2D figures in a hierarchy based on their properties.

Similarity, Right Triangles, and Trigonometry (G.SRT)

• G.SRT.1 Verify by experiment the properties of dilations given by a center and scale factor.
  • a. A dilation maps a line not through the center to a parallel line.
  • b. A dilated segment's length changes by the scale factor.
• G.SRT.2 Use similarity transformations to decide if figures are similar and explain triangle similarity.
• G.SRT.3 Use properties of similarity transformations to establish the AA criterion.
• G.SRT.4 Prove and apply theorems about triangles, including proportional sides and the Pythagorean Theorem by similarity.
• G.SRT.5 Use congruence and similarity criteria to solve problems and prove relationships in figures.
• G.SRT.6 Understand that side ratios in right triangles depend on the angles, defining trig ratios for acute angles.
• G.SRT.7 Explain and use the relationship between sine and cosine of complementary angles.
• G.SRT.8 Solve applied right-triangle problems with trig ratios and the Pythagorean Theorem.
  • a. Solve applied problems given an acute angle and a side length.

Circles (G.C)

• G.C.1 Prove that all circles are similar using transformations.
• G.C.2 Identify and use relationships among angles, radii, chords, tangents and arcs, including inscribed angles.
• G.C.3 Construct inscribed and circumscribed circles of a triangle and prove opposite angles of a cyclic quadrilateral are supplementary.
• G.C.4 Construct a tangent line from a point outside a circle to the circle.
• G.C.5 Find arc lengths and areas of sectors of circles.
  • a. Use similarity to relate arc length to radius and solve problems.
  • b. Derive and use the formula for sector area.

Expressing Geometric Properties with Equations (G.GPE)

• G.GPE.1 Derive the equation of a circle from center and radius and complete the square to find them.
• G.GPE.4 Use coordinates to prove simple geometric theorems, e.g. that a figure is a rectangle.
• G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to write equations of lines.
• G.GPE.6 Find the point on a directed segment that divides it in a given ratio.
• G.GPE.7 Use coordinates and the distance formula to find perimeters of polygons and areas of triangles and rectangles.

Geometric Measurement and Dimension (G.GMD)

• G.GMD.1 Give informal arguments for formulas for circumference, circle area and volumes of cylinders, pyramids and cones.
• G.GMD.3 Use volume formulas for cylinders, pyramids, cones and spheres to solve problems.
• G.GMD.4 Identify cross-sections of 3D objects and solids made by rotating 2D shapes.
• G.GMD.5 Understand how changing lengths or angles gives similar or non-similar figures.
• G.GMD.6 Know that scaling similar figures by k multiplies lengths by k, areas by k² and volumes by k³.

Modeling with Geometry (G.MG)

• G.MG.1 Use shapes, their measures and properties to describe objects, e.g. a tree trunk as a cylinder.
• G.MG.2 Apply density based on area and volume in modeling, e.g. people per square mile.
• G.MG.3 Use geometric methods to solve design problems, e.g. meeting constraints or minimizing cost.