STANDARD COMPETENCIES:

 

 I.      Solve problems in geometry.

 II.     Analyze geometric shapes and measurements.

 III.    Determine perimeter, area, and volume.

 IV.     Prove triangle congruence.

 V.      Appraise parallel lines and quadrilaterals.

 VI.     Determine similarity.

 VII.    Assess circles.

 VIII.   Examine coordinate geometry.

 IX.     Apply transformation geometry.

 TOPICAL OUTLINE:

 

 I.      Solve problems in geometry.

         A.      Use problem-solving strategies on geometric shapes.

         B.      Use problem-solving strategies on sequences.

 II.     Analyze geometric shapes and measurements.

         A.      Use undefined terms, definitions, postulates, segments, and angles.

         B.      Use polygons and axis of symmetry in problem solving.

         C.      Evaluate angles and the sum of angles in polygon or combined polygons.

         D.      Identify and analyze three-dimensional shapes.

         E.      Use dimensional analysis in problem solving.

 III.    Determine perimeter, area, and volume.

         A.      Find perimeter, circumference, area of triangles and rectangles and use strategies to solve combined problems.

         B.      Solve areas of parallelograms, trapezoids, regular polygons, and circles plus use strategies to solve combined problems.

         C.      Use the Pythagorean Theorem to solve problems with right triangles, rectangles and combined problems.

         D.      Find surface area solutions to various polyhedron and spheres.

         E.      Find volume solutions to various polyhedron and spheres.

 IV.     Hypothetical reasoning and triangle congruence.

         A.      Use reasoning strategies to make conclusions from given statements of fact.

         B.      Use triangle congruence to analyze triangles and then write a basic proof of congruence.

         C.      Solve problems using triangle congruence.

         D.      Use a compass and ruler to make basic geometric constructions.

 V.      Appraise parallel lines and quadrilaterals.

         A.      Use postulate and theorem on parallel lines.

         B.      Apply knowledge of parallel lines to solve problems.

         C.      Use properties of parallelograms to solve problems and write proofs.

         D.      Use properties of rectangles, squares, and trapezoids to solve problems and write proofs.

         E.      Use a compass and ruler to make constructions involving parallel lines.

 VI.     Determine similarity.

         A.      Use ratio and proportion to solve problems.

         B.      Use knowledge of proportion and theorems on similarity to solve problems and write proofs.

         C.      Use knowledge of mean proportion in a right triangle, Side Splitting Theorem, and Mid-segment Theorem to solve problems and write proofs.

         D.      Find solutions to right triangles using basic right triangle trigonometry.

 VII.    Assess circles.

         A.      Use knowledge of central and inscribed angles to solve problems and write proofs.

         B.      Find solutions to problems and write proofs using knowledge of chords of a circle.

         C.      Use knowledge of secants and tangents to solve problems and write proofs.

         D.      Use a compass and ruler to make constructions involving circles.

 VIII.   Examine coordinate geometry.

         A.      Find distances on the coordinate plane.

         B.      Use coordinates of a line segment to find its slope.

         C.      Find equations of lines and circles on the coordinate plane.

         D.      Use coordinate knowledge to solve problems.

 IX.     Apply transformation geometry.

         A.      Find solutions to problems using isometries and congruence.

         B.      Find solutions to problems using similitudes and similarity.

         C.      Use the knowledge of transformation to solve geometric problems.