Secondary Geometry Objectives  
                              
       Chapter 1 – Basics of Geometry  
       Students will learn about the basic elements of geometry, including how to use 
       inductive reasoning, how to measure segments and angles, how to bisect a 
       segment or angle, and the relationships among special pairs of angles.  
         • Analyze geometric patterns to develop formulas and communicate how the formulas were 
          derived.  
         • Model and solve geometric situations using algebraic properties.  
         • Find the length, midpoint and slope of a segment given the coordinates of the endpoints.  
         • Use accepted geometric notations.  
         • Identify angle pairs as adjacent, complementary, supplementary, a linear pair, or vertical 
          angles.  
         • Classify angles as acute, right, obtuse or straight.  
         • Constructing angle and segment bisectors  
         • Performing constructions to copy segments and angles.  
         • Finding the area of polygons and circles.  
         • Finding the perimeter and circumference of polygons and circles.  
        
       Chapter 2 – Reasoning and Proof  
       Students will solve problems by recognizing, analyzing, and writing logical 
       arguments.  
         • Write conditional statements, converses, and inverses and determine the truth value of the 
          statements.  
         • Prove a statement false by using a counterexample.  
         • Recognize and complete different styles of proof using deductive reasoning.  
         • Apply reasoning skills to develop an algebraic proof.  
         • Using symbolic notation to form conclusions by applying the laws of logic to true 
          statements.  
        
       Chapter 3 – Perpendicular and Parallel Lines  
       Students will investigate the relationships between lines and angles on a plane 
       and in space.  
         • Write an equation of a line perpendicular or parallel to a line through a given point.  
         • Model and solve geometric situations using algebraic properties.  
         • Recognize parallel or perpendicular lines by analyzing the slope or angle relationships.  
         • Recognize and complete different styles of proof using deductive reasoning.  
         • Differentiate between parallel, perpendicular, skew, and intersecting lines.  
         • Classify angle pairs formed by two lines and a transversal.  
         • Constructing parallel and perpendicular lines.  
        
       Chapter 4– Congruent Triangles  
       Objective: Students will classify and prove triangles congruent given information 
       about their sides and angles.  
         • Model and solve geometric situation using algebraic properties.  
        
         • Prove congruency of geometric figures  
         • Recognize and complete different styles of proof using deductive reasoning.  
        • Classify and use the properties of acute, right, scalene, oblique, isosceles, 
         equilateral, or equiangular triangles.  
       
      Chapter 5– Properties of Triangles  
      Students will investigate the properties of bisectors, medians, altitudes, and mid-
      segments of a triangle and how those properties relate to triangles. Students will 
      also investigate various triangle inequalities.  
        • Model and solve geometric situations using algebraic properties.  
        • Identify medians, altitudes, and angle bisectors of a triangle and the perpendicular 
         bisectors of the sides of a triangle.  
        • Identify and apply the properties of mid-segments of triangles and trapezoids.  
        • Identify and apply the properties of perpendicular bisectors and angle bisectors.  
        • Constructing perpendicular lines through a point.  
        • Constructing points of concurrency.  
       
      Chapter 6– Quadrilaterals  
      Students will study quadrilaterals, their properties and will apply those properties 
      to solve geometric problems.  
        • Model and solve geometric situations using algebraic properties.  
        • Develop reasoning skills to classify a quadrilateral as a parallelogram, trapezoid, 
         rectangle, square, rhombus, kite or none of the above.  
        • Recognize and complete different styles of proof using deductive reasoning.  
        • Identify the properties of polygons and quadrilaterals.  
        • Identify and apply the properties of mid-segments of trapezoids.  
        • Verify the classifications of geometric figures using coordinate geometry to find 
         lengths and slopes.  
       
      Chapter 7 - Transformations  
      Students will learn about transformations, including the three ways to describe 
      motion of geometric figures in the plane and how to use transformations in real-
      life situations.  
        • Identify and define vectors related to transformations.  
        • Perform & analyze transformations (translations, rotations, reflections, and 
         dilations) using coordinate geometry  
        • Translate, reflect, and rotate geometric figures.  
       
      Chapter 8 – Similarity  
      Students will learn about similar polygons, including four ways to prove triangles 
      are similar given information about their sides and angles and how to use similar 
      polygons to solve real-life problems.  
        • Set up ratios and solve proportions for given similar geometric shapes.  
        • Determine the similarity of geometric figures by applying appropriate similarity 
         theorems.  
        • Apply ratios and proportions to solve problems using the properties of similar 
         figures.  
       
        • Solving real-world problems using trigonometric ratios and properties of congruent 
         and similar figures.  
        • Apply Geometric Mean in applications of proportions.  
       
      Chapter 9 – Right Angles and Trigonometry  
      Students will learn about right triangles and trigonometry, including properties 
      related to general right triangles, similar right triangles, and special right 
      triangles. They will also learn applications of right triangles (trigonometry), 
      triangle measurement, and vectors.  
        • Identify trigonometric relationships (sine, cosine, & tangent) using right triangles, 
         expressing the relationships as fractions or decimals.  
        • Solve problems using the properties of special right triangles.  
        • Find the angle measure in degrees given the trigonometric ratio using a calculator.  
        • Find the trigonometric ratio given the angle measure in degrees using a calculator.  
        • Find the missing measures of right triangles.  
        • Solving real-world problems using trigonometric ratios and properties of 
         congruence and similar figures.  
        • Apply Geometric Mean in problems involving proportions.  
       
      Chapter 10 – Circles  
      Students will learn about the properties of segments, angles, and arcs related to 
      circles  
        • Identify the relationships between the measures of intercepted arcs and inscribed 
         or central angles.  
        • Identify radii, diameters, chords, secants, arcs, sectors, central angles, inscribed 
         angles, and tangents for circles.  
        • Writing the equation for a circle given its graph.  
        • Graphing a circle given the equation in the form (x – h)² + ( y – k)² = r²  
       
      Chapter 11 – Area of Polygons and Circles  
      Students will learn about areas of polygons and circles, including how to find 
      angle measures and areas of polygons, how to compare perimeters and areas of 
      similar figures, and how to find the circumference and area of a circle.  
        • Define pi as the ratio of the circumference to the diameter of a circle.  
        • Find the area of polygons and circles.  
        • Find the circumference and arc length of a circle.  
        • Find the area of an irregular region.  
        • Calculate and find the measures of the interior and exterior angles of regular 
         polygons.  
       
      Chapter 12 – Surface Area and Volume  
      Students will learn about surface area and volume of solids, including how to calculate 
      and use surface area and volume of various solids in real-life situations.  
        • Classify regular polyhedrons.  
       
         • Find the surface area and volume for prisms, cylinders, pyramids, cones, and 
          spheres given the formula.  
         • Calculate and find the measures of the interior and exterior angles of regular 
          polygons.