Math 5030 Spring 2009 assignments of weeks 5 to 9:

Week 5:

Due Monday 2/9: Today’s handout on the ideas we are working on.

Due Wednesday 2/11: Do but don’t hand in practice problems 5, 6 of section 9.3 on page 490. Hand in: Use our triangle congruence criteria (some or all of SSS, SAS, ASA) and the fact that the base angles of isosceles triangles are equal (which was proved in class and also in practice problem 5) to prove that (1) the diagonals of a rhombus bisect the angles of the rhombus, [hand this part in on Friday: and (2) the diagonals of a rhombus are perpendicular and bisect each other.]

Due Friday 2/13: Read section 8.5 and do the practice problems in that section. Also do but don’t hand in problems 1a, 2a, and 4 a, b, c, on pages 442, 443. Hand in: (A) Use triangle congruence criteria, the fact that the base angles of an isosceles triangle are equal, and the fact that the diagonals of a rhombus bisect the angles of the rhombus (that you proved in Wednesday’s homework) to prove that the diagonals of a rhombus are perpendicular and bisect each other. (B) Problem 2 on page 301 of the Activity Manual (which asks you to construct an octagon in a circle). Hint: it may help to look back at the “don’t hand in” problems first. Leave all your construction marks. List your steps (no further explanation is needed). You may use Geometer’s Sketchpad instead of a compass and ruler if you prefer.

Week 6:

Due Monday 2/16: First honors credit extra assignment due (this is only for students who are signed up for honors credit). Do but don’t hand in: do all the Georgia Performance Standards 7th grade constructions using only a compass and ruler (scroll down to M7G1). For the constructions of perpendicular lines, be able to construct a line that is perpendicular to a given line through a given point on the line or a given point not on the line. For each construction, be able to explain why the construction works based on either (1) the definition of circle, (2) a triangle congruence criterion (SSS, SAS, ASA), (3) one of the properties of rhombuses that we proved: the diagonals are perpendicular, bisect each other, and bisect the angles of the rhombus, or (4) a property that we proved holds for quadrilaterals whose opposite sides are the same length: the opposite sides of such a quadrilateral are necessarily parallel.

Due Wednesday 2/18: Do but don’t hand in: continue or repeat the “don’t hand in” assignment from Monday. Hand in: Your student proposes the following construction for a square ABCD. Carry out the construction (you may use Geometer’s Sketchpad), determine if this construction will produce a square or not, and discuss why the construction does or doesn’t work. Step 1: Starting with a line segment AB, construct two circles that have AB as a radius, one with center A and one with center B. Step 2: Construct two lines that are perpendicular to segment AB, one line m through point A and one line n through point B. Step 3: Let E be one of the points where the two circles in step 1 intersect. Construct a line p that is parallel line to AB and goes through point E. Step 4: Let C be the point where lines n and p meet and let D be the point where lines m and p meet. The student says that ABCD is a square.

Due Friday 2/20: Read pages 402 – 404 on angles and reflected light and do practice problems 12, 13 of section 8.2. Here is a handout on basic constructions and why they work. QUIZ on (1) applying triangle congruence criteria to explain properties of isosceles triangles, rhombuses, and other quadrilaterals whose opposite sides are the same length; (2) constructions with compass and ruler and why these constructions work based on properties of shapes.

Week 7:

Due Monday 2/23: Hand in: Problem 17 on page 418. You might like to use Geometer’s Sketchpad to produce the drawings for this problem. If so, use a circle for the convex mirror (you will only need a portion of the circle for the mirror). The normal lines for the convex mirror are lines through the center of the circle. Position a line segment representing the flat mirror in roughly the same location as the portion of the circle that you are using for the convex mirror (you might use different colors for the two different mirrors). Use a point for the eye. Compare what the eye sees when looking at a point on the convex mirror versus what it would see when looking at a “comparable point” (i.e., a point roughly in the same location) on a flat mirror by constructing line segments that represent light rays going to the eye.

If you want to read ahead, coming up we will be working on section 9.4, similarity.

Today’s (2/24) episode of Peep and the Big Wide World at http://www.peepandthebigwideworld.com/videos/index.html is about the moon. It’s intended for the really young kids (PreK) but I think it’s adorable and hilarious and it’s a propos of our work earlier in the semester.

Due Wednesday 2/25: Read pages 493, 494 of section 9.4. Monday’s HW may be handed in today.

Due Friday 2/27: Read section 9.4 through page 497 and do practice problems 1 – 4 in section 9.4. Hand in: Problem 3 on page 509 of the text and Class Activity 9U on page 340 of the activity manual: answer the questions in the 2^nd and 3^rd paragraphs and select the method we discussed that will make your calculations easiest.

Week 8:

Due Monday 3/2: Read section 9.4 from page 497 to page 501 (up to “Finding Heights ...”). Do Practice problems 5, 7, 8 of section 9.4. Also do but don’t hand in problems 1, 2, 5, 6 on pages 509, 510. Hand in: Problem 7 a, b on page 510.

Due Wednesday 3/4: QUIZ on the first part of section 9.4, pages 493 – 497. In particular, be able to explain the “scale factor” and “relative sizes” method (in class we called the second method the “internal comparison” or “internal factor” method). Be able to relate those two methods to proportions as in Figure 9.54.

Due Friday 3/6: Read the rest of section 9.4. Do practice problem 9. Hand in: Problem 10 on page 511. Note: your drawing does not have to take a “side view” or a “top view” but could also take a “diagonal view,” e.g., it could take the view of a fly that is up where the wall meets the ceiling.

SPRING BREAK March 9 – 13

Honors credit extra assignment 2 is now posted and due 4/3

Week 9:

Due Monday 3/16: You may hand in the HW due Friday 3/6 if you’d like to work on it over spring break. Do but don’t hand in: For each of the 5 methods we discussed and used to find the height of a tree with similar triangles on Friday 3/6, explain how to use the method and explain why it works. Part of your explanation should include a discussion of why the triangles you claim are similar really are similar. The 5 methods:

(1) Method 1 of class activity 9X on page 344 (shadow of person versus shadow of tree), and see also problem 6 on page 510

(2) “sighting” the tree with a ruler, as in class activity 9W

(3) “sighting” with a card, as described in class

(4) looking into a mirror on the ground to see the tip of the tree

(5) with a camera obscura, as in practice problem 9 on page 504.

If you want to read ahead, coming up we will be working on chapter 10, measurement.

Due Wednesday 3/18: Read section 10.1 and do the practice problems in that section. Hand in: Do EITHER A OR B (pick whichever you think will be most helpful to your future teaching of the ideas in section 10.1). (A) Write a brief summary of section 10.1 by writing a few (1 – 3) sentences for each heading. (B) Pick two ideas/concepts from your reading of section 10.1 that you found especially interesting or important and write a brief paragraph about each one describing what you would want to highlight or emphasize if you were teaching students these ideas/concepts.

Due Friday 3/20: TEST on similarity, section 9.4, and the material discussed between 2/4 and 2/23 on compass and straightedge constructions and applying triangle congruence criteria to explain properties of shapes (especially isosceles triangles and rhombuses) and to explain why compass and straightedge constructions work (sections 9.3, 8.5, part of 8.4, and supplements – see links to handouts on this webpage).