Geometry (Missouri Learning Standards)

Congruence (CO), cluster A

• G.CO.A.1 Define angles, circles, perpendicular and parallel lines, segments, and rays from undefined terms.
• G.CO.A.2 Represent plane transformations as functions that map points to points.
• G.CO.A.3 Describe rotational and line symmetry of flat figures.
• G.CO.A.4 Define rotations, reflections, and translations using angles, circles, and lines.
• G.CO.A.5 Rotate, reflect, or translate figures and find a sequence linking two congruent figures.

Congruence (CO), cluster B

• G.CO.B.6 Define congruence through rigid motions.
• G.CO.B.7 Build the triangle congruence criteria from the rigid-motion definition.

Congruence (CO), cluster C

• G.CO.C.8 Prove theorems about lines and angles.
• G.CO.C.9 Prove theorems about triangles.
• G.CO.C.10 Prove theorems about polygons.

Congruence (CO), cluster D

• G.CO.D.11 Construct figures with a range of tools and methods.

Similarity, Right Triangles, and Trigonometry (SRT), cluster A

• G.SRT.A.1 Construct and analyze dilations of figures.
• G.SRT.A.2 Use the definition of similarity to test figures and solve problems.
• G.SRT.A.3 Use similarity transformations to establish the AA criterion.

Similarity, Right Triangles, and Trigonometry (SRT), cluster B

• G.SRT.B.4 Use triangle congruence and similarity to solve problems and prove relationships.

Similarity, Right Triangles, and Trigonometry (SRT), cluster C

• G.SRT.C.5 Know side ratios in right triangles define the trig ratios of acute angles.
• G.SRT.C.6 Explain and use how sine and cosine of complementary angles relate.
• G.SRT.C.7 Solve right triangles with trig ratios and the Pythagorean Theorem.
• G.SRT.C.8 Derive the triangle area formula A = ½ab sin C.

Circles (C), cluster A

• G.C.A.1 Use similarity transformations to prove all circles are similar.
• G.C.A.2 Describe how inscribed angles, radii, and chords of circles relate.
• G.C.A.3 Construct a triangle's inscribed and circumscribed circles and prove angle facts for quadrilaterals inscribed in circles.

Circles (C), cluster B

• G.C.B.4 Derive the arc length formula.
• G.C.B.5 Derive the sector area formula.

Exploring Geometric Properties with Equations (GPE), cluster A

• G.GPE.A.1 Derive the equation of a circle.
• G.GPE.A.2 Derive the equation of a parabola from its focus and directrix.

Exploring Geometric Properties with Equations (GPE), cluster B

• G.GPE.B.3 Use coordinates to prove geometric theorems algebraically.
• G.GPE.B.4 Prove the slope tests for parallel and perpendicular lines and apply them.
• G.GPE.B.5 Find the point that splits a directed segment in a given ratio.
• G.GPE.B.6 Use coordinates to find polygon perimeters and the areas of triangles and rectangles.

Geometric Measurement and Dimension. (GMD), cluster A

• G.GMD.A.1 Give informal arguments for circle, cylinder, pyramid, and cone formulas.
• G.GMD.A.2 Solve problems with volume formulas for cylinders, cones, pyramids, spheres, and composite solids.

Geometric Measurement and Dimension. (GMD), cluster B

• G.GMD.B.3 Identify the flat cross sections of solids.
• G.GMD.B.4 Identify solids formed by transforming flat shapes.

Modeling with Geometry (MG), cluster A

• G.MG.A.1 Describe real objects with geometric shapes, measures, and properties.
• G.MG.A.2 Use density ideas based on area and volume in modeling.
• G.MG.A.3 Use geometric methods to solve design and modeling problems.

Conditional Probability and Rules of Probability (CP), cluster A

• G.CP.A.1 Describe events as parts of a sample space, or as unions, intersections, or complements.
• G.CP.A.2 Understand independent events and use the idea to solve problems.
• G.CP.A.3 Find conditional probabilities.
• G.CP.A.4 Make and read two-way tables and use them to test independence and estimate conditional probability.
• G.CP.A.5 Explain conditional probability and independence in context.
• G.CP.A.6 Use and interpret the Addition Rule.
• G.CP.A.7 Use and interpret the general Multiplication Rule in uniform probability models.
• G.CP.A.8 Use permutations and combinations to solve problems.