Geometry (Kentucky Academic Standards)

Number and Quantity (N)

• KY.HS.N.5 and KY.HS.N.6 (choosing quantities and suitable accuracy for modeling) are also part of this course; they are listed under Algebra 1.

Geometry (G)

• KY.HS.G.1 Use precise definitions of segments, angles, circles and parallel and perpendicular lines.
  • a. Know the properties of line segments, angles and circles.
  • b. Know the properties of perpendicular and parallel lines and how they differ.
• KY.HS.G.2 Describe transformations as functions of points and compare those that keep distance.
  • a. Understand that transformations take input points to output points.
  • b. Compare transformations that keep distance and angle with those that do not.
  • c. Describe rotations and reflections that map a shape onto itself.
• KY.HS.G.4 Use rigid motions to draw figures, describe sequences and test congruence.
  • a. Draw a figure after a rotation, reflection or translation.
  • b. Give a sequence of transformations that maps one figure onto another.
  • c. Predict the effect of rigid motions and decide congruence from the definition.
• KY.HS.G.5 Use triangle congruence and link it to rigid motions.
  • a. Show triangles are congruent through matching sides and angles.
  • b. Explain how ASA, SAS and SSS follow from rigid motions.
• KY.HS.G.6 Use theorems about lines, angles, triangles and parallelograms.
• KY.HS.G.7 Prove theorems about geometric figures.
  • a. Write formal proofs of theorems about lines, angles and triangles.
• KY.HS.G.8 Make and use geometric constructions.
  • a. Make formal constructions with a range of tools and methods.
  • b. Use basic constructions to build more complex figures.
• KY.HS.G.9 Understand the properties of dilations.
  • a. Check the properties of a dilation given a center and scale factor.
  • b. Check that a dilated image is similar to the original.
• KY.HS.G.10 Use similarity transformations to establish the AA criterion for similar triangles.
• KY.HS.G.11 Use triangle theorems and similarity criteria to solve problems and prove relationships.
  • a. Use theorems about triangles.
  • c. Use similarity criteria to solve problems and prove relationships.
• KY.HS.G.12 Understand right triangles and use trigonometric ratios.
  • a. Define sine, cosine and tangent from similar right triangles.
  • b. Explain how the sine and cosine of complementary angles are related.
  • c. Use trigonometric ratios and the Pythagorean Theorem in applied problems.
• KY.HS.G.15 Use dilations to show that all circles are similar.
• KY.HS.G.16 Describe relationships between angles and segments in circles.
  • a. Tell inscribed, central and circumscribed angles apart and know their properties.
  • b. Relate inscribed angles to a diameter of the circle.
  • c. Relate a radius to the tangent line at the point of tangency.
• KY.HS.G.19 Connect the algebraic and geometric descriptions of a circle.
  • a. Write the equation of a circle from its center and radius.
• KY.HS.G.21 Use coordinates to prove simple geometric theorems algebraically.
• KY.HS.G.22 Justify and use the slope criteria for parallel and perpendicular lines.
• KY.HS.G.23 Find midpoints, distances and dividing points in the coordinate plane.
  • a. Find the midpoint and length of a segment from coordinates.
  • b. Find the point that divides a directed segment in a given ratio.
• KY.HS.G.24 Find perimeters and areas of 2-D figures from coordinates.
  • a. Find the perimeters of polygons.
  • b. Find areas of triangles, rectangles and other quadrilaterals (modeling).
• KY.HS.G.25 Analyze and judge arguments for formulas for figures and solids.
  • a. Justify the formulas for the circumference and area of a circle.
  • b. Justify volume formulas for spheres, prisms, cylinders, pyramids and cones.
• KY.HS.G.27 Use volume formulas to solve problems with cylinders, pyramids, cones, spheres and prisms (modeling).
• KY.HS.G.28 Identify the shapes of cross sections and the solids made by rotating 2-D shapes.
• KY.HS.G.29 Use shapes, their measures and properties to describe real objects.
• KY.HS.G.30 Use density based on area and volume in modeling, with suitable units.
• KY.HS.G.31 Use geometric methods to solve design problems (modeling).