Unit 8 Properties Of Two Dimensional Shapes — Unit Plan

Title	Assessment
Lesson 1 Ways to Look at Figures	What Do They Have in Common? Here are five shapes that have some attributes in common. Select all statements that are true about the attributes they share. Every shape has at least two sides that are the same length. Every shape has at least one right angle. Every shape has at least one pair of parallel sides. Every shape has sides of different lengths. Every shape has at least two angles that are the same size. Show Solution A and E
Lesson 2 Ways to Look at Triangles	Which Would Fit in the Set? Here is a set of triangles that share an attribute and belong together. Which of the following triangles have the same attribute and would also fit in the set? Explain your reasoning. Which of the six triangles are right triangles? Show Solution Sample response: Each triangle has two sides that have the same length (or have two angles that are the same size). Triangle D, because the left and right sides are the same length (or because two of the angles are the same size) Triangle F, because the two longer sides are the same length (or because two of the angles are the same size). Triangles A and E
Lesson 3 Ways to Look at Quadrilaterals	Quadrilaterals Rule Here are four shapes that share some attributes. List two attributes they all share. 4 shapes. all have 4 sides. First shape. 1 pair of parallel sides, non parallel sides are same length, 2 acute angle, 2 obtuse angles. Second shape. 2 pairs of opposite parallel sides, 2 acute angle, 2 obtuse angles. Third shape. 2 pairs of opposite parallel sides, 2 acute angle, 2 obtuse angles. All sides are same length. Fourth shape, 1 pair of parallel sides, non parallel sides are same length, 2 acute angle, 2 obtuse angles. Show Solution Sample responses: All four shapes have: Four sides At least one pair of sides that are the same length At least one pair of parallel sides Two obtuse angles and two acute angles
Lesson 4 Symmetry in Figures (Part 1)	One Line or More than One? Which figures have more than one line of symmetry? Explain or show your reasoning. 4 shapes. A. pentagon, 5 equal side lengths. B. smiley face. C. 24 sided shape. Looks like 4 same size arrows pointing up, down, left, right. D. pentagon, 2 sides forming a right angle. 2 other sides, same length. 5th side much smaller than other 4. Show Solution C is the only one with more than one line of symmetry. All the others have only one line of symmetry.
Lesson 5 Symmetry in Figures (Part 2)	Make Them Whole The shaded figure is half of a whole figure with a line of symmetry, shown by the dashed line. Here's Kiran's drawing to show the whole figure. Do you agree that Kiran's drawing shows the correct whole figure? Explain or show your reasoning. If you disagree, you can also show the correct whole figure by drawing. Show Solution Disagree. Sample response: If Kiran's drawing is folded along the dashed line, the two halves don't match up exactly. The correct whole figure should look like this:
Lesson 6 All Kinds of Attributes	Can You See It? Here are diagrams that each show a pair of intersecting segments. Add 1 or more segments to each diagram to make a figure that has: 1. 1 line of symmetry 2. 2 or more lines of symmetry 3. no lines of symmetry Show Solution Sample responses: 1. 2. 3.
Section A Check Section A Checkpoint	Problem 1 Which of the triangles are right triangles? Explain or show your reasoning. dot paper with 3 triangles. Triangle A. horizontal side, 3, vertical side, 3. Triangle B. horizontal side, 3, vertical side, 3. Triangle C, horizontal side 4, other two sides equal length forming an obtuse angle. Show Solution Sample response: Triangle A is a right triangle because the angle at the top right is a right angle. Triangle B is a right triangle because the angle at the bottom left is a right angle. Triangle C is not a right triangle because it does not have any right angles. Problem 2 Draw a shape that is a rectangle but not a rhombus. Label it A. Draw a shape that is a rhombus but not a rectangle. Label it B. Show Solution Sample response: Problem 3 Draw all lines of symmetry for each figure. Show Solution

Lesson 7 Ways to Find Unknown Length (Part 1)	What's the Perimeter? Here is a rectangle with two lines of symmetry. Find its perimeter. Write an expression to show how you find it. Show Solution 84 mm. Sample response: $17 + 17 + 25 + 25$ , or $(2 \times 17) + 25 + 25$
Lesson 8 Ways to Find Unknown Length (Part 2)	Stage Symmetry A stage at a concert is shaped like the letter Y and has 3 lines of symmetry. Its perimeter is 56 yards. Draw the lines of symmetry. Find the length of the sides labeled Y and Z. Explain or show your reasoning. Show Solution See drawing. Y is $8\frac{1}{3}$ yards and Z is 2 yards. Sample response: The lines of symmetry tell us that the 6 long sides are equal and the 3 short sides are equal. $6 \times 8\frac{1}{3} = 50$ and $56 - 50 = 6$ . Since 3 times Z is 6, Z must be 2 yards.
Lesson 9 Symmetry in Action	Fold It Once A piece of paper is folded once along a line of symmetry. The result of folding is this triangle with three equal sides. What could be the original shape of the paper, before it was folded? Draw a sketch and show the line of symmetry. Write an expression for the perimeter of that original shape. Show Solution Sample responses: Sample responses: $5\frac{1}{2} + 5\frac{1}{2} + 5\frac{1}{2} + 5\frac{1}{2}$ or $4 \times 5\frac{1}{2}$
Lesson 10 Ways to Find Angle Measurements	Stage Symmetry: Revisited Find the measurement of Angles P, Q, R, and S. Explain or show your reasoning. Show Solution Angle P is $120^\circ$ . Angles S and Q are both $90^\circ$ . Angles R is $60^\circ$ . Sample response: The figure has 3 lines of symmetry. Angle P matches the $120^\circ$ angle on the other side of the line of symmetry. Angle S matches up with the right angle on the other side of the triangle. Angle Q matches up with the right angle next to it. Angles P, Q, R, and S add up to $360^\circ$ . $\text{P} + \text{Q} + \text{S} = 120 + 90 + 90 = 300$ , so R is $360 - 300$ , which is 60.
Lesson 11 Symmetry in Sports	No cool-down
Section B Check Section B Checkpoint	Problem 1 This figure has one line of symmetry. What is the perimeter of the shape? Explain or show your reasoning. Show Solution 78 inches. Sample response: The line of symmetry tells me the unlabelled side is 24 inches and $12 + 18 + 24 + 24 = 78$ . Problem 2 This shape has 4 lines of symmetry and a perimeter of 36 cm. What is the length of each of the sides? Explain or show your reasoning. Show Solution 9 cm. Sample response: If the shape has 4 lines of symmetry, then the 4 side lengths are all equal. 36 cm divided by 4 is 9 cm for each side or $9+9+9+9=36$ .