Conditional Statements Geometry Notes And Homework

Geometry Curriculum

Unit 6 Triangle Parts

      Unit 6 Homework Schedule      

      Point of concurrency Graphic Organizer Blank

      Points of Concurrency Graphic Organizer Key

      Powerpoint Notes

            ** 6.1 Perpendicular and Angle Bisectors ppt

            ** 6.1 Perpendicular and Angle Bisectors pdf

            ** 6.2 - 6.3 Triangle Concurrency Points ppt

            ** 6.2 - 6.3 Triangle Concurrency Points pdf

            ** 6.4 Midsegment Theorem ppt

            ** 6.4 Midsegment Theorem pdf

            ** 6.5 - 6.6 Inequalities in Triangles and Hinge Theorem ppt

            ** 6.5 - 6.6 Inequalities in Triangles and Hinge Theorem pdf

 

Unit 2  Reasoning and Proofs

Unit 2 Reference Page

Unit 2 Reference Page Answers

 

Powerpoints:

         ** 1.1 Points, Lines, and Planes

         ** 1.2 Measuring and Constructing Segments

         ** 1.3 Using Midpoint and Distance Formulas

         ** 1.4  Perimeter and Area in the Coordinate Plane

         ** 1.5 Measuring and Constructing Angles

         ** 1.6 Describing Pairs of Angles

Unit 11 Area, Perimeter, Circumf., Surface Area & Volume

           Powerpoint Notes:

           ** 11.1 Circumference and Arc Length ppt

           ** 11.1 Circumference and Arc Length  pdf

           ** 11.2 Area of Circles and Sectors  ppt

           ** 11.2 Area of Circles and Sectors pdf

           ** 11.3A  Quadrilateral & Triangle Area Formulas (Squares, Rectangles, Parallelograms, Triangles, Trapezoids, Rhombuses, and Kites)  ppt

           ** 11.3A Quadrilateral & Triangle Area Formulas (Squares, Rectangles, Parallelograms, Triangles,
    Trapezoids, Rhombuses, and Kites)  pdf

           ** 11.3B Area of Regular Polygons ppt

          ** 11.3B Area of Regular Polygons pdf

         ** 11.4 Thee-Dimensional Figures ppt    

         ** 11.4  Three-Dimensional Figures pdf

                11.4 Exploration Page

                11.4 Exploration link: 

          **  11.5  Volumes of Prisms and Cylinders ppt

          **  11.5 Volume of Prism and Cylinders pdf

           ** 11.6  Surface Areas and Volumes of Pyramids and Cones ppt

           ** 11.6  Surface Areas and Volumes of Pyramids and Cones  pdf

            ** 11.7  Surface Areas and Volumes of Spheres ppt

 

            ** 11.7  Surface Areas and Volumes of Spheres pdf

 

Unit 10 Properties of Circles

      Powerpoint Notes:
          ** 10.1 Lines and Segments in Circles ppt

          ** 10.1 Lines and Segments in Circles pdf            

          ** 10.2 Finding Arc Measure ppt

          ** 10.2 Finding Arc Measure  pdf

          ** 10.3 Unsing Chords ppt

          ** 10.3 Unsing Chords  pdf

         ** 10.4  Inscribed Angles and Polygons ppt

          ** 10.4  Inscribed Angles and Polygons pdf

          ** 10.5 Angle Relationships in Circles  ppt

          ** 10.5 Angle Relationships in Circles  pdf

          ** 10.6 Segment Relationships in Circles  ppt

          ** 10.6 Segment Relationships in Circles  pdf

           **10.7  Circles in the Coordinate Plane  ppt

           **10.7  Circles in the Coordinate Plane  pdf

Unit 9 Right Triangles and Trigonometry

         Powerpoint Notes:

               * 9.1 The Pythagorean Theorem  ppt

               * 9.1 The Pythagorean Theorem  pdf

               * 9.2 Special Right Triangles  ppt

               * 9.2 Special Right Triangles  pdf

               * 9.3  Similar Right Triangles  ppt

               * 9.3  Similar Right Triangles  pdf

               * 9.4  Trigonometric Ratios - Tangent  ppt

               * 9.4  Trigonometric Ratios - Tangent  pdf

               * 9.5  Trigonometric Ratios - Sine and Cosine  ppt

               * 9.5  Trigonometric Ratios - Sine and Cosine  pdf

               * 9.6  Solving Right Triangles  ppt

               * 9.6  Solving Right Triangles  pdf

               * 9.7  Law of Sines and Law of Cosines  ppt

               * 9.7  Law of Sines and Law of Cosines  pdf

 

 

Unit 8 Similarity

 Unit 8 Homework Schedule
  Powerpoint Notes:

       ** 8.1 Similar Polygons ppt

       ** 8.1 Similar Polygons pdf

      ** 8.2 Proving Triangle Similarity  by AA ppt

       ** 8.2 Proving Triangle Similarity  by AA  pdf

      ** 8.3 Proving Triangles Similarity by SSS and SAS  ppt

      ** 8.3 Proving Triangles Similarity by SSS and SAS  pdf

      ** 8.4  Proportionality Theorems  ppt

      ** 8.4  Proportionality Theorems  pdf

 

Unit 7 Polygons and Quadrilaterals

   Unit 7 Test Reference Sheet (BLANK)

   Unit 7 Test Reference Sheet (KEY) doc

   Unit 7 Test Reference Sheet (KEY) pdf

      Powerpoint Notes

           ** 7.1 Angles of Polygons ppt

           ** 7.1 Angles of Polygons pdf

           ** 7.2 Properties of Parallelograms ppt

           ** 7.2 Properties of Parallelograms pdf

           ** 7.3 Proving a Quadrilateral is a Parallelogram ppt

           ** 7.3 Proving a Quadrilateral is a Parallelogram pdf

           ** 7.4 Properties of Special Parallelograms ppt

           ** 7.4 Properties of Special Parallelograms pdf

           ** 7.5 Properties of Trapezoids and Kites ppt

           ** 7.5 Properties of Trapezoids and Kites pdf

Unit 5 Congruent Triangles 

     Powerpoint Notes (ppt) ; PDF Notes (pdf)

         ** 5.1  Angles and Triangles ppt

          ** 5.1  Angles and Triangles pdf      

         ** 5.2  Congruent Polygons ppt

         ** 5.2  Congruent Polygons pdf

         ** 5.3 & 5.5 Proving Triangle Congruence by SSS and SAS ppt

         ** 5.3 & 5.5 Proving Triangle Congruence by SSS and SAS pdf

         ** 5.6 Proving Triangle Congruence by ASA and AAS ppt

         ** 5.6 Proving Triangle Congruence by ASA and AAS pdf

         ** 5.4 Isosceles, Equilateral, and Right Triangles and Hypot-Leg (HL) ppt

         ** 5.4 Isosceles, Equilateral, and Right Triangles and Hypot-Leg (HL) pdf

         ** 5.7 Using Congruent Triangles (CPCTC) ppt

         ** 5.7 Using Congruent Triangles (CPCTC) pdf

 

Unit 4 Transformations

Unit 4 Homework Assignments

    Powerpoint Notes

         ** 4.0 Introduction: Rigid Motion in a Plane

         ** 4.1 Translations

         ** 4.2  Reflections

         ** 4.3  Rotations

      Unit 4 Quiz Corrections Key

         ** 4.4  Congruence and Transformations

         ** 4.5  Dilations

         Unit 4 Reference Page with Formulas for Transformations

Unit 3 Parallel and Perpendicular Lines

  Powerpoint Notes

         ** 3.1 / 3.2 Pairs of Lines and Angles / Parallel Lines and Transversals

         ** 3.3  Proofs with Parallel Lines

         ** 3.4 Proofs with Perpendicular Lines

         ** 3.5 Equations of Parallel and Perpendicular Lines (3 Days)

 

 

Unit 9 stuff

Introducing Trig Functions

 

 Unit 7 Homework Schedule

      Quadrilateral Graphic Organizer Blank

      Quadrilateral Graphic Organizer Key!!

 

Unit 5 Congruent Triangles

Unit 5 Homework Assignments

Unit 5 in class Warm Ups

Unit 4 Transformations

Unit 4 Homework Assignments

    Powerpoint Notes

         ** 4.0 Introduction: Rigid Motion in a Plane

         ** 4.1 Translations

         ** 4.2  Reflections

         ** 4.3  Rotations

      Unit 4 Quiz Corrections Key

         ** 4.4  Congruence and Transformations

             4.4 Congruent and Transformations ppt

         ** 4.5  Dilations

             4.5 Dialations ppt

         **  4.6  Similarity and Transformations

 

        **  Unit 1 Quiz Correction Worksheet pdf  (solutions to sample problems)

Unit 3 Homework Assignements

Unit 3 Quiz Correction KEY (for the sample problems)

     Unit 3 Warm - Ups 

        * Warm - Ups for 3.1 - 3.3

        * Warm - Ups for 3.3 - 3.5

 

Converse, Inverse, Contrapositive

Given an if-then statement "if , then ," we can create three related statements:

A conditional statement consists of two parts, a hypothesis in the “if” clause and a conclusion in the “then” clause.  For instance, “If it rains, then they cancel school.” 
  "It rains" is the hypothesis.
  "They cancel school" is the conclusion.

To form the converse of the conditional statement, interchange the hypothesis and the conclusion.
      The converse of "If it rains, then they cancel school" is "If they cancel school, then it rains."

To form the inverse of the conditional statement, take the negation of both the hypothesis and the conclusion.
      The inverse of “If it rains, then they cancel school” is “If it does not rain, then they do not cancel school.”

To form the contrapositive of the conditional statement, interchange the hypothesis and the conclusion of the inverse statement. 
      The contrapositive of "If it rains, then they cancel school" is "If they do not cancel school, then it does not rain."

Statement If , then .
Converse If , then .
Inverse If not , then not .
Contrapositive If not , then not .

 

If the statement is true, then the contrapositive is also logically true. If the converse is true, then the inverse is also logically true.

Example 1:

Statement If two angles are congruent, then they have the same measure.
Converse If two angles have the same measure, then they are congruent.
Inverse If two angles are not congruent, then they do not have the same measure.
Contrapositive If two angles do not have the same measure, then they are not congruent.

 

In the above example, since the hypothesis and conclusion are equivalent, all four statements are true. But this will not always be the case!

Example 2:

Statement If a quadrilateral is a rectangle, then it has two pairs of parallel sides.
Converse If a quadrilateral has two pairs of parallel sides, then it is a rectangle. (FALSE!)
Inverse If a quadrilateral is not a rectangle, then it does not have two pairs of parallel sides. (FALSE!)
Contrapositive If a quadrilateral does not have two pairs of parallel sides, then it is not a rectangle.

 

 

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