ACADEMIC GEOMETRY
updated January 2010



UNIT
Standards
Objectives
1 Tools of Geometry
M11.D.1.1
Analyze and/or use patterns or relations
M11.B.2.1
Use and /or compare measurements of angles
M11.C.3.1
Solve problems using analytic geometry
M11.B.2.2
Use and/or develop procedures to determine or describe measures of perimeter, circumference, area, surface area and/or volume
§ Use inductive reasoning to make conjectures
§ Understand basic terms and postulates of geometry
§ Identify segments and rays and parallel lines
§ To find lengths of segments
§ To find measures of angles
§ Identify special angle pairs
§ Find the distance and midpoint of a segment on a coordinate plane
§ Find perimeter and area of rectangles and squares
§ Find the circumference and area of a circle
2. Triangle Relationships
M11.C.1.2
Recognize and/or apply properties of angles, triangles and quadrilaterals
M11.C.1.4
Solve problems involving right triangles using the Pythagorean Theorem.
  • Classify triangles by their sides and by their angles.
  • Find angles measures in triangles.
  • Use properties of isosceles and equilateral triangles.
  • Use the Pythagorean Theorem and the Distance Formula.
  • Use the Converse of Pythagorean Theorem.
  • Use side lengths to classify triangles.
  • Identify medians in triangles
  • Use triangle measurements to decide which side is longest and which angle is largest.
3. Segments and Angles
M1 1 .C.3.1
Solve problems using analytic geometry.
M11.C.1.2
Recognize and/or apply properties of angles, triangles and quadrilaterals
M1 1 .C.1 .3
Use properties of congruence, correspondence and similarity in problem-solving settings involving two- and three- dimensional figures
  • Bisect a segment.
  • Find the coordinates of the midpoint of a segment.
  • Bisect an angle.
  • Find measures of complementary and supplementary angles.
  • Find measures of angles formed by intersecting lines.
  • Use properties of equality and congruence
4. Parallel and Perpendicular Lines
M11.C.1.2
Recognize and/or apply properties of angles, triangles and quadrilaterals
  • Identify relationships between lines.
  • Use theorems about perpendicular lines.
  • Identify angles formed by transversals.
5. Right Triangles and Trigonometry
M1 1 .A.2.2
Use exponents, roots and/or absolute value to solve problems.
  • Simplify square roots.
  • Find the side lengths of 45-45-90 triangles.
  • Find the side lengths of 30-60-90 triangles.
6. Quadrilaterals
M11.C.1.2
Recognize and/or apply properties of angles, triangles and quadrilaterals
  • Identify and classify polygons
  • Find angle measures of quadrilaterals
  • Use properties of parallelograms
  • Determine if a quadrilateral is a parallelogram
  • Use properties of the rhombus, rectangle, and square.
7. Similarity
M1 1 .A.2.1
Apply ratio and/or proportion in problem-solving situations.
M11.C.1.3Use the Triangle Proportionality Theorem Use properties of congruence, correspondence and its converse and similarity in problem-solving settings involving Identify and draw dilations two- and three- dimensional figures.
  • Use ratios and proportions
  • Identify similar polygons
  • Use the AA, SSS, and SAS Similarity Postulates to show that two triangles are similar
8. Surface Area and Volume
M11.B.2.2
Use and/or develop procedures to determine or describe measures of perimeter, circumference, area,
surface area and/or volume.
  • Identify and name solid figures
  • Find the surface area of prisms, cylinders, pyramids, and cones
  • Find the volume of prisms, cylinders, pyramids, and cones
  • Find the surface area and volume of spheres
9. Circles
M1 1 .C.1 .1
Identify and/or use parts of circles and segments associated with circles.
M11.B.2.1
Use and/or compare measurements of angles.
  • Use properties of arcs of circles to identify angle and arc measures.
  • Find arc length
  • Use the properties of inscribed angles
  • Identify rotations and rotational symmetry