High School Geometry (Alaska Standards)

Congruence

• G-CO.1 Define angle, circle, perpendicular and parallel lines and segment from the undefined terms point, line, distance and arc.
• G-CO.2 Represent transformations as functions on points and compare rigid motions with others such as stretches.
• G-CO.3 Describe the rotations and reflections that map a rectangle, parallelogram, trapezoid or regular polygon onto itself.
• G-CO.4 Define rotations, reflections and translations using angles, circles, perpendicular and parallel lines and segments.
• G-CO.5 Draw the image of a figure under a rotation, reflection or translation and specify sequences of moves.
• G-CO.6 Use rigid motions to transform figures, predict effects and decide whether two figures are congruent.
• G-CO.7 Use rigid motions to show triangles are congruent exactly when corresponding sides and angles are congruent.
• G-CO.8 Explain how the ASA, SAS, SSS, AAS and HL congruence tests follow from defining congruence with rigid motions.
• G-CO.9 Prove theorems about lines and angles using methods such as direct proof, indirect proof and counterexamples.
• G-CO.10 Prove theorems about triangles (angle sum, isosceles base angles, midsegment, medians) using a range of proof methods.
• G-CO.11 Prove theorems about parallelograms and their converses, including rectangles, using a range of proof methods.
• G-CO.12 Make formal constructions with compass and straightedge, paper folding or software (copying, bisecting, perpendiculars, parallels).
• G-CO.13 Construct an equilateral triangle, square and regular hexagon inscribed in a circle.

Similarity, Right Triangles, & Trigonometry

• G-SRT.1 Check by experiment the properties of dilations with a center and scale factor.
• G-SRT.2 Use similarity transformations to decide if figures are similar and explain similarity of triangles through matching angles and proportional sides.
• G-SRT.3 Use similarity transformations to establish the AA similarity criterion.
• G-SRT.4 Prove triangle theorems such as the side-splitter theorem and the Pythagorean Theorem using 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, leading to the trigonometric ratios.
• G-SRT.7 Explain and use how sine and cosine of complementary angles are related.
• G-SRT.8 Solve right triangles in applied problems with trig ratios and the Pythagorean Theorem.
• G-SRT.9 (+) Derive the triangle area formula A = ½ab sin C.
• G-SRT.10 (+) Prove the Law of Sines and the Law of Cosines and apply them.
• G-SRT.11 (+) Apply the Laws of Sines and Cosines to find unknown sides and angles in any triangle.

Circles

• G-C.1 Prove that all circles are similar.
• G-C.2 Describe relationships among inscribed, central and circumscribed angles, radii and chords, including tangent and radius.
• G-C.3 Construct a triangle's inscribed and circumscribed circles and prove angle facts for cyclic quadrilaterals.
• G-C.4 (+) Construct a tangent from an outside point to a circle.
• G-C.5 Use similarity to show arc length is proportional to radius, define radians and derive the sector area formula.

Expressing Geometric Properties with Equations

• G-GPE.1 Derive the equation of a circle from the Pythagorean Theorem and complete the square to find center and radius.
• G-GPE.2 Derive the equation of a parabola from a focus and directrix.
• G-GPE.3 (+) Derive equations of ellipses and hyperbolas from their foci.
• G-GPE.4 Prove simple geometry theorems algebraically with coordinates.
• G-GPE.5 Prove the slope tests for parallel and perpendicular lines and apply them to problems.
• G-GPE.6 Find the point that divides a directed segment in a given ratio.
• G-GPE.7 Use coordinates (e.g. the distance formula) to find polygon perimeters and triangle and rectangle areas.

Geometric Measurement & Dimension

• G-GMD.1 Explain how to find the circumference and area of a circle and the volume of a cylinder, pyramid and cone.
• G-GMD.2 (+) Use Cavalieri's principle informally to justify the sphere volume formula and others.
• G-GMD.3 Use the volume formulas of common solids (cylinder, pyramid, cone, sphere) in problems, including finding a missing dimension.
• G-GMD.4 Identify 2-D cross-sections of 3-D objects and 3-D objects formed by rotating 2-D shapes.

Modeling with Geometry

• G-MG.1 Use shapes and their measures to describe real objects (e.g. a tree trunk as a cylinder).
• G-MG.2 Use density by area or volume in modeling (e.g. people per square mile).
• G-MG.3 Use geometric methods to solve design problems with physical limits or cost goals.