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Grade 7_Quarter 1- Polygons
Table of Contents
- Lesson 1: Polygons as composite figures
- Activity 1.1 Composing Polygons Using Triangles
- Activity 1.2 Decomposing Polygons into Triangles
- Lesson 2: Drawing polygons
- Activity 2.1 Reading Measures of Angles in Protractor
- Activity 2.2 Measuring Angles using Protractor
- Activity 2.3 Drawing Angles
- Activity 2.4 Drawing Polygons with GeoGebra
- (Optional) Activity 2.5 Drawing Polygons (using protractor and segment with a given length tool)
- (Optional) Activity 2.5: Drawing Polygons with other GeoGebra Tools
- (Optional) Activity 2.5: Drawing Polygons (using protractor and ruler))
- Lesson 3: Categorizing polygons based on properties
- Activity 3.1 Classifying Polygons
- Activity 3.2 Describing Polygons
- Lesson 4: Angles in polygons
- Activity 4.1 Interior and Exterior Angles of Polygons
- Activity 4.2 Exterior Angles of Convex Polygons
- Lesson 5: Applying properties of polygons in problem solving
- Activity 5.1: Exterior Angles - Drill #1
- Activity 5.2: Exterior Angles - Drill #2
- Activity 5.3: Exterior Angles - Drill #3
- Activity 5.4: Exterior Angles - Drill #4
- Lesson 6: Angle pairs in polygons
- Activity 6: Angle Pairs in Polygons
- Lesson 7: Applying angle relationships in problem solving
- Activity 7.1: Angle Pairs - Problem Set #1
- Activity 7.2: Angle Pairs - Problem Set #2
- Activity 7.3: Angle Pairs - Problem Set #3
- Activity 7.4: Angle Pairs - Problem Set #4
- Lesson 8: Sum of interior angles of polygons
- Activity 8: Sum of Interior Angles of Polygons
- Lesson 9: Solving problems involving polygons
- Activity 9.1: Polygons and Angles - Problem Set #1
- Activity 9.2: Polygons and Angles - Problem Set #2
- Activity 9.3: Polygons and Angles - Problem Set #3
- Activity 9.4: Polygons and Angles - Problem Set #4
Activity 1.1 Composing Polygons Using Triangles
YOUR TASK
Form or [b]compose[/b] polygons such as triangles, squares, and parallelograms using triangles, [b]describe[/b] your process, and [b]justify[/b] why you think you have composed the required polygons.
A.1 COMPOSE a triangle
Use two or more triangles to compose at least one bigger triangle in the applet below. Type the name of the new triangle.
You can drag or rotate these triangles to compose new figures. Use the [color=#ff00ff]pink [/color]vertex to drag the triangle and the [color=#0000ff]blue [/color]vertex to rotate it.
A.2 DESCRIBE
Write your step-by-step process to form a new triangle from the given triangles. Write it in a way that others can follow the process on their own. [br][color=#0000ff]Isulat kung ano ang iyong mga naging hakbang para makagawa ng bagong triangle mula sa mga nakalaan. Isulat ito para madaling masundan ng iba.[/color]
A.3 JUSTIFY
Provide reasons why you think the polygon you composed above is a triangle.[br][color=#0000ff]Ipaliwanag kung paano ka nakasigurado na iyong na-compose ay isa ngang triangle.[/color]
B.1 COMPOSE a square
Use 2 triangles to compose at least one square. Type the name or names of the squares you formed.
B.2 JUSTIFY
Explain why you are sure that the polygon you composed is a square.
C.1 COMPOSE a parallelogram
Use 2 or more triangles to compose a parallelogram. Type the name of the parallelogram formed.
C.2 JUSTIFY
Explain why you are sure that the polygon you formed or composed is a parallelogram.
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Co-developer
Erlina Ronda
Activity 2.1 Reading Measures of Angles in Protractor
YOUR TASK
[b]Determine[/b] the measurement of angles using the protractor and [b]describe[/b] your method.
This GeoGebra applet randomly generates angles. Read the measure of each angle and type your answer in the corresponding input box. A checkmark will indicate a correct response. You can click the "Get New Angle" button to generate new angles and click the "Restart" button to start with the basic angles.
Angles named AOB will appear as you generate the angles. Write [b]at least three strategies[/b] you used to determine the measure of AOB.
DESCRIBE strategies
Write your strategy for finding the measure of angle AOB.
Write another strategy for finding the measure of angle AOB.
Write another strategy for finding the measure of angle AOB.
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Activity 3.1 Classifying Polygons
YOUR TASK
Study the given polygons. Note how they are similar or different. [b]Classify[/b] them according to their[b][i] common characteristics[/i][/b]. You may start with 3 categories.
The GeoGebra applet in this activity includes various types of polygons. You can [b]drag[/b] the [b][color=#38761d]green vertex[/color][/b] of each polygon to place them in the appropriate category boxes.[br][br]
IDENTIFYING common characteristics
What characteristics is common to all the polygons under category #1?
What characteristics is common to all the polygons under category #2?
What characteristics is common to all the polygons under category #3?
NAMING categories
Based on the common characteristics you identified, how will you name[br][br]Category #1?[br]Category #2?[br]Category #3?
EXTEND
Think of other ways of classifying the polygons? Use the GeoGebra applet below to explore other ways to categorize the polygons
What characteristics is common to all the polygons under category #4?
What characteristics is common to all the polygons under category #5?
What characteristics is common to all the polygons under category #6?.
NAMING categories
Based on the common characteristics you identified, how will you name[br][br]Category #4?[br]Category #5?[br]Category #6?
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Erlina Ronda
Activity 4.1 Interior and Exterior Angles of Polygons
YOUR TASK
Explore and identify the relationships between the angles formed by intersecting lines.[br]Determine if the statements of relationships between angles is ALWAYS TRUE or ALWAYS FALSE
This GeoGebra applet shows a quadrilateral ABCD with the measure of its interior angle shown. [br][br]To explore, click the button to show the figure when the sides are extended. You can also change the figure by [color=#0000ff]dragging[/color] any of the [b][color=#0000ff]points [/color][/b]A, B, or C. Each time you drag any of the points, you will have a different set of angle measurements. [br][br]To identify the relationships among the angles, record the measurements of the angles in the table. [br][br]
Generate sets of measure for interior and exterior angles of quadrilateral ABCD.
TRUE or FALSE, JUSTIFY
For each of the statement below,[br][br][b]Write TRUE [/b]if the statement is always true. Then, justify your answer using the data in the table.[br][br][b]Write FALSE[/b] if the statement is always false or not true. Then, justify using a counterexample from the table.
Sum of interior angles
[i]The sum of the four interior angles of the quadrilateral is 360 degrees. [/i][i]ALWAYS TRUE or ALWAYS FALSE? Justify your answer with examples from the table.[/i]
Sum of a pair of interior and exterior angles with common vertex
[i]The sum of a pair of interior and exterior angles in quadrilateral ABCD is 180 degrees. [/i][i]ALWAYS TRUE or ALWAYS FALSE? Justify your answer with examples from the table.[/i]
Pair of interior angles
[i]The sum of any pair of interior angles in quadrilateral ABCD is 180 degrees. ALWAYS TRUE or ALWAYS FALSE? Justify your answer with examples from the table.[/i]
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[url=https://forms.gle/wFFPJEB65iuTn6MVA][size=100][size=150]Feedback Form[/size][/size][/url]
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Activity 5.1: Exterior Angles - Drill #1
Solve for the exterior angle of each polygon on the figure.
Click the checkbox to solve for each type of polygon. [br]Then, click the "New Polygon" button to generate a new one.[br][br]Solve for the indicated [b][i]exterior angle or interior angle [/i][/b]on the figure. Type your answer in the input box. [br]A checkmark will appear if the measurement is correct. [br][br][br][br]
1. Exploring Relationships Between Interior and Exterior Angles
In the polygons presented, what relationship do you observe between the interior[br]and exterior angles at each vertex? Can you explain why this relationship holds[br]for all polygons, regardless of the number of sides?
2. Exploring the Relationship Between Exterior and Interior Angles in Triangles
[b]2.A.[/b] Look at the triangles shown in the applet and focus on any of the triangle’s exterior angles. [br]Can you describe how this exterior angle is related to the two non-adjacent (or remote) interior angles of the triangle? Use specific angle measures from the triangles to support your explanation.[br][br]
[b]2.B.[/b] Make a general statement relating an exterior angle of a triangle to the interior angles remote to that exterior angle. Justify your statement.
3. Predicting the Exterior Angle Measurement
Before using the applet to find the exterior angle, predict the measure of the[br]exterior angle of a vertex in a regular polygon (like a triangle or a square). [br]Explain your reasoning. [br][br]After predicting, use the applet to check your prediction. Was your reasoning correct? Why or why not?
4. Generalizing Angle Sum Rules
Using the applet, calculate the sum of the interior angles for the given quadrilateral and pentagon. [br]Based on your calculations, derive a general formula to calculate the sum of the interior angles for any polygon with 'n' sides. [br][br]How does this formula relate to the exterior angle measures?
Activity 6: Angle Pairs in Polygons
The sides of the following polygons can be extended.[i][b] Click the checkboxes[/b][/i] to show the [b]extended sides [/b]and the [b]angles formed[/b]. Additional angles can also be constructed using the segment [icon]/images/ggb/toolbar/mode_segment.png[/icon]and angle [icon]/images/ggb/toolbar/mode_angle.png[/icon]tools.[br][br][b]Identify pairs of angles[/b] with [b]specific relationships based on their positions or measures[/b].
Angle Pair #1
Determine one angle pair.
Angle Pair #1 - Description
Describe the relation of Angle pair #1 based on their positions or measures.
Angle Pair #2
Determine another angle pair.
Angle Pair #2 - Description
Describe the relation of the angle pair based on their positions or measures.
Angle Pair #3
Determine another angle pair.
Angle Pair #3 - Description
Describe the relation of the angle pair based on their positions or measures.
Angle Pair #4
Determine another angle pair.
Angle Pair #4 - Description
Describe the relation of the angle pair based on their positions or measures.
Angle Pair #5
Determine another angle pair.
Angle Pair #5 - Description
Describe the relation of the angle pair based on their positions or measures.
Activity 7.1: Angle Pairs - Problem Set #1
Angle pairs in a rectangle and line segments from its extended sides
Solve for the missing angles on the figures. A checkmark will appear if your answer is correct.[br][br]Click the "New Set" button to generate a new problem within that set of questions.
Activity 8: Sum of Interior Angles of Polygons
Description of the GeoGebra applet:
This GeoGebra applet enables you to select the number of sides for the polygon, ranging from three (3) to twelve (12), by adjusting the slider.
Task
For each polygon, use the line segment tool to decompose it into triangles. Then, determine the sum of the interior angles of each polygon using your prior knowledge of the sum of the interior angles of a triangle. Record each sum in the table below the applet.[br][br]Finally, determine the [b][i]formula for the [color=#1155cc]sum of interior angles[/color] of an [color=#1155cc]n-sided polygon.[/color] [/i][/b]
Scratchwork
Using the data from the table above, determine the formula for the sum of interior angles of an n-sided polygon. [br][br]Use the GeoGebra note for solutions and other scratchwork.
Sum of Interior Angles of a Polygon
What is the formula for the sum of interior angles of an n-sided polygon?
Activity 9.1: Polygons and Angles - Problem Set #1
Click the checkbox to display each set of questions.[br][br]Study the figure and read the given conditions. Solve for the missing angles on the figures. A checkmark will appear if your answer is correct.[br][br]Click the "New Figure" button to generate a new figure within that set of questions.