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5th Grade

Geometry

2015-11-23

www.njctl.org

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Geometry Unit Topics

· Coordinate Plane

· First Quadrant

· Polygons

Click on the topic to go to that section

· Classifying Triangles & Quadrilaterals

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Polygons

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Examples of polygons and figures that are not polygons

These are polygons These are not polygons

Polygons

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This is not a polygon.It is open, not closed.

This is not a polygon.The sides cross over.

This is not a polygonNot all sides are straight.

click to reveal

click to reveal

click to reveal

Shapes That Are Not Polygons

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A polygon is a simple, closed plane figure made up of 3 or more line segments.

Simple - line segments do not intersect (remember, line segments are straight, not curved)

Closed - When you trace the figure, it ends at the starting point.

Plane figure - a two-dimensional (flat) shape

Polygons

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1 Is this figure a polygon?

Yes

No

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Yes

No

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Yes

No

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Yes

No

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Yes

No

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Polygons are named by their number of sides.

Name Number of Sides

Triangle 3

Quadrilateral 4

Pentagon 5

Hexagon 6

Heptagon 7

Octagon 8

Nonagon 9

Decagon 10

Polygons

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3 sides

3 angles

10 sides

10 angles

Polygons

Interesting fact: A polygon's number of sides and number of angles are always the same.

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6 How many sides does a heptagon have?

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7 How many angles does a nonagon have?

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8 Name the figure.

A QuadrilateralB HexagonC DecagonD Octagon

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9 Name the figure.

A DecagonB HexagonC NonagonD Octagon

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Regular vs. Irregular Polygons

If the figure's sides and angles are congruent, it is called a regular polygon.

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Regular vs. Irregular Polygons

If either the figure's sides or angles are not congruent, it is called an irregular polygon.

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10 What kind of polygon is this?

A regularB irregularC not a polygon

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Classifying Triangles &

Quadrilaterals


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By Sides

Equilateral TriangleAll sides are congruent.

Isosceles TriangleAt least two sides are congruent.

Scalene Triangle No sides are congruent.

Match the picture to the definition

TrianglesClassifying Triangles- Triangles can be classified by their angles or their sides.

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16 Classify the triangle by its sides

A equilateral

B scalene

C isosceles

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17 Classify the triangle by its sides

A equilateral

B scalene

C isosceles

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By Angles

Acute TriangleAll three angles are less than 90 degrees.

Right TriangleOne angle is 90 degrees.

Obtuse Triangle One angle is more than 90 degrees.

Match the picture to the definition

Triangles

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18 Classify the triangle by its angles

A acute

B obtuse

C right

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A acute

B obtuse

C right

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A acute

B obtuse

C right

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Click to go to web site then choose Triangle Sort.

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21 Classify the triangle.

A equilateral

B isosceles

C scalene

D acute

E right

F obtuse

Remember: Classify by sides and angles (put in two answers)

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A equilateral

B isosceles

C scalene

D acute

E right

F obtuse


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http://www.crickweb.co.uk/ks2numeracy-shape-and-weight.html#




23 If each of the angles in a triangle measures 60 º , what is the triangle?

A equilateral

B isosceles

C scalene

D acute

E right

F obtuse


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A equilateral

B isosceles

C scalene

D acute

E right

F obtuse


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25 Classify the triangle in the yield sign.

A equilateral

B isosceles

C scalene

D acute

E right

F obtuse


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26 Classify the triangle this bridge makes.

A equilateral

B isosceles

C scalene

D acute

E right

F obtuse


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Quadrilaterals

Classifying QuadrilateralsYou must use the properties of quadrilaterals

to identify and classify them.

Trapezoids - Exactly one pair of parallel sides.

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Parallelogram - Opposite sides are congruent & parallel.

Quadrilaterals

Interesting fact: The opposite angles of a parallelogram are also congruent.



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Similar to triangles, quadrilaterals are classified by the relationships between their sides and angles.

Rectangle - Special parallelogram with four right angles

Quadrilaterals

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Rhombus - Parallelogram with four congruent sides and opposite angles congruent

Quadrilaterals

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Square - Rhombus with four right angles or a Rectangle with four congruent sides .

Quadrilaterals

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Match the shape with the description.

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Square

RectangleRhombus

Parallelogram

Trapezoid

Quadrilateral

one pair of // sides

two pairs of // sides

all angles ~=all sides ~=

all angles ~=all sides ~=

two pairs of // sides

two pairs of // sidestwo pairs of // sides

4-sided polygon

4-sided polygon

4-sided polygon

4-sided polygon4-sided polygon

4-sided polygon

Quadrilaterals

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Polygon

Quadilateral

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Polygon

Quadilateral

Trapezoid

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Quadilateral

Trapezoid

Parallelogram

Polygon

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Quadilateral

Trapezoid

Parallelogram

Rectangle

Polygon

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Quadilateral

Trapezoid

Parallelogram

Rectangle Rhombus

Polygon

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Quadilateral

Trapezoid

Parallelogram

SquareRectangle Rhombus

Polygon

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Click for web site and then choose polygon sort.

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From PARCC EOY sample test #13

Drag and drop the names to complete the diagram that shows the relationship among the figures listed. Each category will be used only once.

rhombuses rectanglesparallelograms quadrilaterals

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27 Which of the following shapes is a trapezoid?

A B

C D

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28 Which of statement(s) do NOT describe the figure?

A trapezoidB parallelogramC rectangleD rhombusE square

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http://epat-parcc.testnav.com/client/index.html#tests

29 Which of the statements does NOT describe the figure?


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30 Which of the statement(s) does NOT describe the figure?


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31 Which of the following statements is true?

A A square is not a rectangle.

B A rectangle is a square.

C A square is not a parallelogram.

D A square is a rectangle.

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32 Which shape has exactly one pair of // sides?

A square

B rhombus

C triangle

D trapezoid

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33 Which shape has two sets of congruent angles and adjacent sides congruent?

A square

B rectangle

C rhombus

D kite

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34 Describe the figure. Choose all answers that apply.

A QuadrilateralB TrapezoidC ParallelogramD RectangleE RhombusF SquareG None of the Above

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38 Describe the shape of the top of the desk. Choose all answers that apply.


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39 Describe the shape for the face of the clock. Choose all answers that apply.


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40 Describe the shape of the mouth of the shark. Choose all answers that apply.


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41 Describe the shape of this marker. Choose all answers that apply.


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42 Which of the following shapes could never have perpendicular sides?

A rectangleB triangleC circleD square

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43 Which of these shapes could never have parallel opposite sides?

A trapezoidB triangleC rectangleD rhombus

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44 Which explanation about figures is correct? A All rhombuses are parallelograms. Parallelograms

have 2 pair of parallel sides. Therefore, all rhombuses have 2 pairs of parallel sides.

B All rhombuses are parallelograms. Parallelograms have exactly 1 pair of parallel sides. Therefore, all rhombuses have exactly 1 pair of parallel sides.

C Only some rhombuses are parallelograms. Parallelograms have 2 pairs of parallel sides. Therefore, only some rhombuses have 2 pair of parallel sides.

D Only some rhombuses are parallelograms. Parallelograms have exactly 1 pair of parallel sides. Therefore, only some rhombuses have exactly 1 pair of parallel sides.


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45 Select an answer for each blank.

Because a ________ is a ________, it must have 4 A square B rectangle C trapezoid

D squareE rectangleF rhombus

opposite angles ≅ and all four sides ≅.

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Coordinate Plane


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The coordinate plane is formed by two intersecting number lines called axes.

The horizontal line is the x-axis. The vertical line is the y-axis.

Coordinate Plane

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The point at which the x and y axes intersect is called the origin. The coordinates of the origin are (0, 0).

Origin(0, 0)

Coordinate Plane

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(x,y)

x

yCoordinate Plane

Points can be plotted on the plane using one coordinate from each of the axes. These sets are called ordered pairs. The x coordinate always appears first in these pairs. The y coordinate appears second.

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(4,3)

To graph an ordered pair, such as (4,3):· Start at the origin (0,0).· Move right on the x-axis, since the first number is positive.· Then, move up since the second number is positive. · Plot the point.

Coordinate Plane

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(x,y)

x

y

This point is (3,2).To plot the point, go over 3, then up 2.

Coordinate Plane

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(x,y)

x

y


Coordinate Plane

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(x,y)

x

y


Coordinate Plane

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x

y46 Which point is at the origin?

A B

CD

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x

y47 Which point is at (1,3)?

A B

CD

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x


A B

CD

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x


A B

CD

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50 Which ordered pair is the origin?

A (4,0)

B (0,0)

C (0,4)

D (4,4)

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51 Which number in the ordered pair (7,3) is the x-coordinate?

A 7

B 3

C 0

D x

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52 Which number in the ordered pair (5,9) is the y-coordinate?

A 0

B 5

C 9

D y

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53 Which number in the ordered pair (7,12) is the y-coordinate?

A 7

B 12

C 0

D y

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54 Which number in the ordered pair (7,12) is the x-coordinate?

A 7

B 12

C 0

D x

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55 Select three statements that correctly describe the coordinate system.

A The x- and y-axes intersect at 10.

B The x- and y-axes intersect at the origin.

C The x- and y-axes are parallel number lines.

D The x- and y-axes are perpendicular number lines.

E The x- and y-axes are used to locate points on a coordinate plane.


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Mia is playing several rounds of a word game. Each coordinate pair shows the number of the round and Mia's score fore that round. She is keeping track of these coordinate pairs on a graph.· Round 1: (1, 3)· Round 2: (2, 6)· Round 3: (3, 3)Part A

Graph Mia's scores for the first three rounds of play. Move the 3 points to their location on the graph.

A B C

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56 Part B

In round 4, Mia scores the same number of points as in rounds 2 and 3 combined. What is the coordinate pair that represents Mia's score for round 4?

A (4, 5)

B (9, 4)

C (5, 4)

D (4, 9)


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57 The following points were graphed on the coordinate plane. Select the correct letter that corresponds with each point on the graph.

A

B

C

D

E

F

1. (4,6)

2. (6,4)

3. (3,0)

(A or B)

(B or C)

(D or E)

A

BC

D

E


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First Quadrant


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First Quadrant

First Quadrant

When the x and y coordinates are both positive, points are plotted in the first quadrant.

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Play Billy Bug and His Quest for Grub Game

Click for web site.

http://resources.oswego.org/games/BillyBug/bugcoord.html

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First Quadrant

Sometimes we are asked to create a shape in the first Quadrant by finding the missing point....

Try these examples.

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58 Which point will create a square?

A (3,2)

B (5,1)

C (2,1)

D (1,2)

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59 Which point will create a right triangle?

A (1,4)

B (4,1)

C (3,4)

D (2,1)

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60 Which point will create a parallelogram?

A (4, 8)B (8, 4)

C (9, 5)

D (7, 4)

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61 Which point will create a trapezoid?

A (1, 3)

B (1, 1)C (3, 3)D (3, 1)

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62 Emily drew a figure on a coordinate grid. The figure has one pair of opposite sides that are parallel, but not equal. Which of the following figures could Emily have drawn?

A

B

C

D

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63 Chose an answer to fill in each blank.Point A is _____ units ____________ to the x-axis

and _____ units ______ to the y-axis than point C.

A 2 B 5 C 7

D closer to E further from

F 2 G 5 H 7

I closer to J further from

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89

10

02 3 4 5 6 7 8 9 101

7

A

B

C

D

E

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64 Chose an answer to fill in each blank.Point D is _____ units ____________ to the x-axis

and _____ units ______ to the y-axis than point B.

A 2 B 3 C 4

D closer to E further from

F 2 G 3 H 4

I closer to J further from

123456

89

10

02 3 4 5 6 7 8 9 101

7

A

B

C

D

E

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12345

02 3 41

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65 The coordinate plane shows the number of customers the Ice Cream Shoppe had in the first 3 weeks of June. If the pattern continues, how many customers will they have during the 4th week of June?

A 5

B 6

C 55

D 60

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12345

02 3 41

# of

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66 The coordinate plane shows the number of customers the Ice Cream Shoppe had in the first 3 weeks of September. If the pattern continues, how many customers will they have during the 5th week of September?

A 15

B 20

C 25

D 30

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Click above to practice using theNational Library of Virtual Manipulatives web site.

This example, the vertices are:(1,3)(4,1)(4,3)

· Work in partners.· One partner creates a polygon on the geoboard and writes down the vertices.· Other partner plots the points, and connects them with line segments.· Compare the polygons, then switch roles.

Coordinate Grid Geoboards Activity

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http://nlvm.usu.edu/en/nav/frames_asid_166_g_2_t_3.html?open=activities&from=category_g_2_t_3.html

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