### Geometry

This is a traditional geometry course recommended for students who intend to pursue a 4-year college degree. Geometry is one of the most interesting, creative, and useful branches of mathematics. The topics covered in this class include a study of deductive reasoning and proof, triangles, quadrilaterals, other polygons, geometric solids, and probability.
Note: Standards Identifiers auto-link to popup a detailed description and links to Proficiency Scales with Prioritized Standards Identifiers being highlighted a sky-blue.

## MAT-10.GM (GM) Geometry

• MAT-10.GM.01    Know precise definitions and notations of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, and plane.
• MAT-10.GM.02    Represent transformations in the plane. Describe transformations as functions taking points in the plane as inputs and giving other points as outputs. Compare transformations that preserve distance and angle to those that do not (i.e., rigid versus non-rigid motion).
• MAT-10.GM.03    Describe the rotations and reflections of a triangle, rectangle, parallelogram, trapezoid, or regular polygon that map each figure onto itself or another figure.
• MAT-10.GM.04    Develop or verify the characteristics of rotations, reflections, and translations in angles,circles, perpendicular lines, parallel lines, and line segments.
• MAT-10.GM.05    Draw the image of a figure that has undergone a series of transformations [rotation(s),reflection(s), or translation(s)] of a geometric figure using a variety of methods (e.g., graph paper, tracing paper, or geometry software).
• MAT-10.GM.06    Predict the effect of a specified rigid motion on a given figure using geometric descriptions of rigid motions. Determine whether two figures are congruent using the definition of congruence in terms of rigid motions.
• MAT-10.GM.07    Use the definition of congruence, based on rigid motions, to show two triangles are congruent if and only if their corresponding sides and corresponding angles are congruent.
• MAT-10.GM.08    Prove two triangles are congruent using the congruence theorems.
• MAT-10.GM.09    Prove and apply theorems about lines and angles.
• MAT-10.GM.10    Prove and apply theorems about triangles.
• MAT-10.GM.11    Prove and apply theorems about parallelograms.
• MAT-10.GM.12    Make basic geometric constructions(e.g., segment, angle, bisectors, parallel and perpendicular lines) with a variety of tools and methods.
• MAT-10.GM.13    Apply basic constructions to create polygons such as equilateral triangles, squares, and regular hexagons inscribed in circles.
• MAT-10.GM.14    Verify experimentally and justify the properties of dilations given by a center and a scale factor.
• MAT-10.GM.15    Use transformations to decide if two given figures are similar. Apply the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
• MAT-10.GM.16    Prove similarity theorems about triangles.
• MAT-10.GM.17    Apply knowledge of congruence and similarity criteria for triangles to solve problems and to prove relationships in various geometric figures.
• MAT-10.GM.18    Recognize how the properties of similar right triangles allow the trigonometric ratios to be defined and determine the sine, cosine, and tangent of an acute angle in a right triangle.
• MAT-10.GM.19    Explain and use the relationship between the sine and cosine of complementary angles.
• MAT-10.GM.20    Solve applied problems involving right triangles using trigonometric ratios, the Pythagorean Theorem, and special right triangles(30°-60°-90° and 45°-45°-90°).
• MAT-10.GM.21    Solve unknown sides and angles of non-right triangles using the Laws of Sines and Cosines.
• MAT-10.GM.22    Apply theorems about relationships between line segments and circles or angles and circles formed by radii, diameter, secants, tangents,and chords to find unknown lengths or angles.
• MAT-10.GM.23    Construct the incenter and circumcenter of a triangle. Relate the incenter and circumcenter to the inscribed and circumscribed circles.
• MAT-10.GM.24    Construct a tangent line from a point outside a given circle to the circle.
• MAT-10.GM.25    Explain and use the formulas for arc length and area of sectors of circles.
• MAT-10.GM.26    Recognize that the radian measure of an angle is the ratio of the length of the arc to the length of the radius of a circle.
• MAT-10.GM.27    Develop and verify the slope criteria for parallel and perpendicular lines. Apply the slope criteria for parallel and perpendicular lines to solve problems.
• MAT-10.GM.28    Verify simple geometric theorems algebraically using coordinates. Verify algebraically, using coordinates, that a given set of points produces a particular type of triangle or quadrilateral.
• MAT-10.GM.29    Determine the midpoint or endpoint of a line segment using coordinates. (+) Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
• MAT-10.GM.30    Compute perimeters of polygons and areas of triangles, parallelograms, trapezoids, and kites using coordinates.
• MAT-10.GM.31    Explain derivations of the formulas for the circumference of a circle, area of a circle, and volume of a cylinder, pyramid, and cone.
• MAT-10.GM.32    Calculate the surface area for prisms, cylinders, pyramids, cones, and spheres to solve problems.
• MAT-10.GM.33    Know and apply volume formulas for prisms, cylinders, pyramids, cones, and spheres to solve problems.
• MAT-10.GM.34    Identify the shapes of two-dimensional cross-sections of three-dimensional objects and identify three-dimensional objects generated by rotations of two-dimensional objects.
• MAT-10.GM.35    Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).
• MAT-10.GM.36    Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; scaling a model).

## MAT-10.DPS(DPS) Data Probability and Statistics

##### (DA) Data Analysis
• MAT-10.DPS.01    Represent data with plots on the real number line (dot plots, histograms, and box plots).
• MAT-10.DPS.02    Compare the center (median, mean)and spread (interquartile range, standard deviation) of two or more different data sets using statistics appropriate to the shape of the data distribution.
• MAT-10.DPS.03    Represent data on two quantitative variables on a scatter plot and describe how the variables are related.
• MAT-10.DPS.04    Distinguish between correlation and causation.
##### (P) Probability
• MAT-10.DPS.05    Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes or as unions, intersections, or complements of other events (“or,” “and,” “not”).
• MAT-10.DPS.06    Recognize that event A is independent of event B if the probability of event A does not change in response to the occurrence of event B. Apply the formula P(A and B) = P(A)·P(B) given that events A and B are independent.
• MAT-10.DPS.07    Recognize that the conditional probability of an event A given B is the probability that event A will occur given the knowledge that event B has already occurred. Calculate the conditional probability of A given B and interpret the answer in context.
• MAT-10.DPS.08    Apply the formula P(A or B) = P(A) + P(B) – P(A and B) and interpret the answer in context.
• MAT-10.DPS.09    Determine the number of outcomes using permutations and combinations in context.
• MAT-10.DPS.10    Construct and interpret two-way frequency tables of data for two categorical variables. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.