Geometry Journal Entries

11.1: Your 5th grade students are learning to use protractors to measure angles.  Several of your students measured the angle below as 130°. a) Why do you believe the students are incorrectly reporting the measurement of 130°? b) How could you enable your students to see why their measurement is incorrect?  What exactly would you say to the student? (be specific)

11.2: a) Compare and contrast figure A with figure B (below).  (Note: Compare means to tell how they are alike.  Contrast means to tell how they are different.) b) Explain why every square is a rectangle but not every rectangle is a square.

13.1: Your student, Shelly, measured the segment pictured below as 1.4 inches. a) What do you believe Shelly’s reasoning was that led to this response? b) Explain to Shelly WHY her answer is incorrect and how she should use the ruler to correctly find the measurement.

11.3: In class we saw that the sum of the interior angles for a convex n-gon can be found using the formula (n-2)180.  Explain in your own words why this formula works.

11.4: Compare and contrast a square-based prism with a square-based pyramid.  Include a drawing of each.

12.1: Construct with a straightedge and compass an angle that is congruent to the angle below.  Include a written description of the steps you take.

12.2: Explain in your own words why “ASS” is not enough information for showing two triangles are congruent.  Include example triangles to support your reasoning.  Triangles should be accurately drawn.

12.3: Provide a written description of the steps taken in constructing an angle bisector.  How is this process related to a rhombus and its properties?

12.4: Explain why 2 square are always similar but 2 rectangles are not always similar.

13.2: Many people incorrectly believe that since there are 3 feet in one yard, there are also 3 square feet in a square yard.  Provide a conceptually-based explanation of why this is not true.  Be sure to include drawings to support your explanation.

13.3: a) Explain how to find the length of the side labeled x in the triangle below. b) Find the perimeter and area of the triangle. c) If you triple the length of each side of the triangle, what do you believe will happen to the perimeter?  To the area? d) Test your conjecture from part c.  Were you correct?  Why do you believe you obtained these results?

13.4: What is meant by the phrase “surface area”?  Explain how to find the surface area of a rectangular prism.  Include an example.

13.5: Fran reported that the volume of her cone was 50 inches.  Explain to Fran why it is incorrect to report volume in inches.  Include with your explanation a description of what a cubic inch looks like and what it means to have a volume of 50 cubic inches.

14.1: Examine the pre-image and the image of the equilateral triangle.  Explain how you know that the image is not the result of a translation.  Explain how you know it is the result of a rotation.

14.2: Examine the pre-image and the image from the previous entry.  Explain how you know that the image in not the result of a reflection.

14.4: Compare and contrast rotational symmetry and point symmetry.

14.5: Provide a thorough explanation of why a regular pentagon will not tile a plan.

14.3: Will the image of perpendicular line under a size transformation always be perpendicular lines?