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RM - collect the resource box and homework check sheets and report slip. Send someone to pick up books. Facilitators - get everyone checking their homework. Remind them to show corrections. ™ Keep an eye on the time, need to Return report paper before time runs Out and then team needs to be listening. RR - fill in homework report and return to me. 24 Oct 2018 Agenda - Homework check and report submitted - Lesson 3.1.4 Facts about Isosceles - Learning Log - 3.1.5 Using Transformations to make polygons - 3.51 - 3.1.6 - Must do: 3-61,3-62, 3-65 (finish at home) - Homework 3-44 Facts about Isosceles Triangles a) Copy the B diagram and then draw A’B, the of AB across line l A A’

l 3-44 Facts about Isosceles Triangles

When points A B and A’ are connected, what special polygon is formed by A A’ points A, B and A’? 3-44 Facts about Isosceles Triangles

When points A B and A’ are This is an connected, what isosceles special polygon . is formed by A A’ points A, B and A’? 3-44 Facts about Isosceles Triangles b) What can we say about B this triangle?

A A’ 3-44 Facts about Isosceles Triangles

The triangle has two equal B sides since reflection is a rigid transformation.

A A’ 3-44 Facts about Isosceles Triangles

The line of reflection makes angle with point B and the B line segment BA that is the same as the angle between the line of reflection and BA’

A A’ 3-44 Facts about Isosceles Triangles

The angles opposite the B equal sides are also equal to each other (congruent).

A A’ 3-44 Facts about Isosceles Triangles

The line of reflection divides B the third side into two equal pieces, and it is to that side.

A A’ Little LEARNING LOG 3-44 Isosceles Triangles B Isosceles triangles always have two sides that are equal in length, and the base angles (opposite the equal A A’ sides) are equal. 3.1.5 Using Transformations to Create Polygons In Lesson 3.1.4 you practiced reflecting, rotating, and translating polygons. Since these were rigid transformations, the image always had all the same angle measures and side lengths as the original. In this lesson, you will combine the image with the original to make new, larger polygons from four basic “building block” polygons. As you create new shapes, consider what information the transformation gives you about the resulting new shape. 3-51 The Shape Factory The Shape Factory, an innovative new company, has decided to branch out to include new shapes. As product developers, your team is responsible for finding exciting new shapes to offer your customers. The current company catalog is shown... Since your boss is concerned about production costs, you want to avoid buying new machines and instead want to reprogram your current machines. The factory machines cannot only make all the shapes shown in the catalog, but are also able to rotate or reflect a shape exactly one time. For example, if the half- is rotated 180o about the midpoint of its longest side, as shown, the result is ... The factory machines cannot only make all the shapes shown in the catalog, but are also able to rotate or reflect a shape exactly one time. For example, if the half-equilateral triangle is rotated 180o about the midpoint of its longest side, as shown, the result is a . Your Task: Your boss has given your team until …. to find as many new shapes as you can. Your team’s reputation, which has suffered recently from a series of blunders, could really benefit from an impressive new line of shapes formed by a triangle and its transformations. Your Task: cont. For each triangle in the catalog, determine which new shapes are created when it is rotated OR reflected EXACTLY ONE TIME so that the image shares an entire side with the original triangle. Be sure to make as many new shapes as possible. Use tracing paper to help. Mrs. D-B’s suggestions: All make some rough sketches in your notebooks.

Check you haven’t made the same shape twice. Each person in the team make one cut out sample using colored or white paper. ( See sample for rectangle from Mrs. Day-Blattner).

If you need Further Guidance - you can use 3-52 on page 140 to break the task down even further. Fresh New shapes coming to you from Team … Rectangle Produced by rotating a right triangle about the midpoint of its longest side. The new has 2 sets of parallel sides, with pairs of parallel sides having the same lengths. The vertices of the shape are all 90 degree angles. 3.1.5 Symmetry You have encountered symmetry several times in this chapter. So far you have seen how symmetry arises from some transformations. Now we will look at this relationship between transformations and symmetry further, and this will deepen your understanding of symmetry. By the end of the lesson, you should be able to answer these questions:

What is symmetry? How can you determine whether or not a polygon has symmetry? What types of symmetry can a shape have? 3-61 Reflection Symmetry A figure has reflection symmetry if a reflection carries it onto itself. See an example of a quilt design that has reflection symmetry at right. 3-61 Reflection Symmetry a) Which of the shapes on the resource page have reflection symmetry?

Draw all the possible lines of symmetry (use tracing paper if you like). 3-61 Reflection symmetry

a) regular , , rectangle, equilateral triangle, , isosceles right triangle, , , , isosceles , regular 3-61 Reflection Symmetry regular hexagon 3-61 Reflection Symmetry 3-61 Reflection Symmetry rectangle, equilateral triangle, square, isosceles right triangle, circle, isosceles triangle, , regular pentagon 3-61 Reflection symmetry

b) triangles with reflection symmetry equilateral triangle, isosceles right triangle, isosceles triangle 3-61 c) Which types of have reflection symmetry? square, rectangle, rhombus, kite, And isosceles trapezoid 3-61 d) Which shapes on your resource page have more than three lines of symmetry? square, regular pentagon, regular hexagon, and circle 3-62 Rotation Symmetry a) Is this shape a polygon? 3-62 a) Is this shape a polygon? Yes b) Can this figure be rotated onto itself? If so where is the center (point) of rotation? let's see 3-62 a) Is this shape a polygon? Yes b) and it can be rotated onto itself (see desmos demonstration) using the center of the shape as the center of rotation. Rotate 120 degrees or any multiple of it. (360 divided by 3 is 120) 3-62 c) Jessica claims that she can rotate all polygons in such a way that they will not change. How does she do it? 3-62 c) Jessica claims that she can rotate all polygons in such a way that they will not change. How does she do it? Rotate 360 degrees! (All the way around until the shape is back where it started.) 3-62 d) Since all polygons can be rotated 360° without change, that is not a very special quality. However, the polygon in part (a) above was special because it could be rotated less than 360° and still remain unchanged. A polygon with this quality is said to have rotation symmetry.

But what shapes have rotation symmetry? From resource page - Regular hexagon, rectangle, equilateral triangle, square, circle, rhombus, , and regular pentagon. 3-62 e) Circle and square have 90 degree rotation symmetry (can be rotated about a point 90° and remain unchanged). 3-63 Translation symmetry a. Is there a polygon that can be translated so that its end result is exactly the same as the original object? If so, draw an example and explain why it has translation symmetry.

b. Is there any kind of shape or figure that has translation symmetry?

3-63 Translation symmetry

a. Is there a polygon that can be translated so that its end

result is exactly the same as the original object? If so, draw an example and explain why it has translation symmetry.

There are no polygons that can be translated and still be exactly the same as the original object. 3-63 Translation symmetry

b)Is there any kind of shape or figure that has translation symmetry?

Lines can be translated so that the end result is exactly the

same as the original. Also, a tessellation that extends infinitely in all directions can be translated so that the end result is exactly the same as the original.

3-64 Describing symmetry a. What reflections carry this decagon onto itself? Describe its lines of reflection. If this polygon has no reflection symmetry, explain how you know. b. What rotations carry this polygon onto itself? (Describe a point of rotation and angles for which this polygon has rotation symmetry.) 3-64 a. The decagon has 10 lines of symmetry which pass through opposite vertices and the midpoints of opposite sides of the polygon. b. The polygon can be rotated about its center (which can be found by finding the point of intersection of the diagonals connecting opposite vertices). The angle of rotation can be 36° or any multiple thereof (notice, 360 divided by 10 is 36). 3-64 C) There is no translation that moves a regular decagon onto itself, so it does not have translation symmetry. As soon as I slide the shape it is not in the same place anymore and is not exactly as it was. 3-65 ? 3-65 Symmetries?

Translation Rotation 180 degrees 3-65 Symmetries?

Reflection across y-axis 3-65 Symmetries?

Reflections Translation rotation 3-65 Symmetries?

Reflections rotation 3-65 Symmetries?

Translation rotation 3-65 Symmetries?

Reflection 3-65 Symmetries? b) If the y-axis is a line of symmetry of a graph, then its function is referred to as even. Which of the graphs in part (a) are even functions? 2) and 6) 3-65 Symmetries? c) If the graph has rotation symmetry about the origin (0, 0), its function is called odd. Which of the graphs in part (a) are odd functions? 3 and 4 Homework

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