Topic: Lines and angles 
Engineering Education 
 Standard 12. Understands the techniques, tools, and technologies related to the production of technical drawings 
  Level IV (Grade 912) 
   Benchmark 8.  Knows procedures for creating geometric constructions (e.g., arcs, angles, bisecting lines, perpendicular and parallel lines, geometric shapes)

    Knowledge/skill statements 
     1.  Knows procedures for creating geometric constructions such as arcs 
     2.  Knows procedures for creating geometric constructions such as angles 
     3.  Knows procedures for creating geometric constructions such as bisecting lines 
     4.  Knows procedures for creating geometric constructions such as perpendicular and parallel lines 
     5.  Knows procedures for creating geometric constructions such as geometric shapes 
   Benchmark 15.  Uses equipment required for drafting and design (e.g., Tsquare, protractor, ruler, drawing instrument, triangles, compass)

    Knowledge/skill statements 
     1.  Uses a Tsquare for drafting and design 
     2.  Uses a protractor for drafting and design 
     3.  Uses a ruler for drafting and design 
     4.  Uses drawing instruments for drafting and design 
     5.  Uses triangles for drafting and design 
Mathematics 
 Standard 4. Understands and applies basic and advanced properties of the concepts of measurement 
  Level II (Grade 35) 
   Benchmark 1.  Understands the basic measures perimeter, area, volume, capacity, mass, angle, and circumference 
    Knowledge/skill statements 
     4.  Understands the concept of angle 
   Benchmark 2.  Selects and uses appropriate tools for given measurement situations (e.g., rulers for length, measuring cups for capacity, protractors for angle) 
    Knowledge/skill statements 
     15.  Selects appropriate tool to measure angles 
     16.  Uses a protractor to measure angles 
 Standard 5. Understands and applies basic and advanced properties of the concepts of geometry 
  Level II (Grade 35) 
   Benchmark 6.  Understands characteristics of lines (e.g., parallel, perpendicular, intersecting) and angles (e.g., right, acute) 
    Knowledge/skill statements 
     1.  Understands the concept of intersecting lines 
     2.  Understands the concept of perpendicular lines 
     3.  Understands the concept of parallel lines 
     4.  Understands the concept of an obtuse angle 
     5.  Understands the concept of an acute angle 
     6.  Understands the concept of a right angle 
  Level III (Grade 68) 
   Benchmark 1.  Uses geometric methods (i.e., an unmarked straightedge and a compass using an algorithm) to complete basic geometric constructions (e.g., perpendicular bisector of a line segment, angle bisector) 
    Knowledge/skill statements 
     1.  Uses a straight edge and compass to construct angle bisectors 
     2.  Uses a straight edge and compass to construct perpendicular bisectors 
     3.  Understands the concept of geometric constructions 
     4.  Understands the concept of an angle bisector 
     5.  Understands the concept of a perpendicular bisector 
  Level IV (Grade 912) 
   Benchmark 1.  Understands that objects and relations in geometry correspond directly to objects and relations in algebra (e.g., a line in geometry corresponds to a set of ordered pairs satisfying an equation of the form ax + by = c) 
    Knowledge/skill statements 
     1.  Understands a line in geometry corresponds to a set of ordered pairs 
     3.  Knows that ax + by = c is the general equation for a line 
   Benchmark 3.  Uses synthetic (i.e., pictorial) representations and analytic (i.e., coordinate) methods to solve problems involving symmetry and transformations of figures (e.g., problems involving distance, midpoint, and slope; determination of symmetry with respect to a point or line) 
    Knowledge/skill statements 
     1.  Uses synthetic geometric models to solve slope problems 
     2.  Uses synthetic geometric models to solve line symmetry problems 
     4.  Uses synthetic geometric models to solve distance problems 
     7.  Uses analytic methods to solve slope problems 
     8.  Uses analytic methods to solve line symmetry problems 
     10.  Uses analytic methods to solve distance problems 
     11.  Uses analytic methods to solve midpoint problems 
   Benchmark 5.  Uses geometric constructions (e.g., the parallel to a line through a given point not on the line, line segment congruent to a given line segment) to complete simple proofs, to model, and to solve mathematical and realworld problems 
    Knowledge/skill statements 
     1.  Constructs a line segment congruent to a line segment 
     3.  Constructs a line through a given point not on the line 
     4.  Uses a line segment congruent to given line segment in proofs 
   Benchmark 10.  Uses inductive and deductive reasoning to make observations about and to verify properties of and relationships among figures (e.g., the relationship among interior angles of parallel lines cut by a transversal) 
    Knowledge/skill statements 
     3.  Understands the concept of a transversal 
   Benchmark 11.  Uses properties of and relationships among figures to solve mathematical and realworld problems (e.g., uses the property that the sum of the angles in a quadrilateral is equal to 360 degrees to square up the frame for a building; uses understanding of arc, chord, tangents, and properties of circles to determine the radius given a circular edge of a circle without the center) 
    Knowledge/skill statements 
     1.  Determines whether a problem can be solved by making use of the relationships among angles 
     2.  Understands the concept of a chord 
     3.  Determines whether a problem can be solved by using chords 
     6.  Understands the concept of a tangent to a circle 
     7.  Determines whether a problem can be solved by using tangents to a circle 
     8.  Determines whether a problem can be solved by using radii 
     12.  Determines whether a problem can be solved by using diameters 