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STRATEGIC

INTERVENTION

MATERIAL

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Prepared by:

Asakil, Flordeliza V.

Casumbal, Epifania J.

Dela Cruz, Lorena O.

Pagulayan, Rowena H.

Reluba, Ma. Theresa C.

Unida, Francisca R.

RIZAL HIGH SCHOOL

SY 2011 - 2012

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How to use this Strategic Intervention Material (SIM)?

• Keep this material neat and clean.

• Thoroughly read every page.

• Follow carefully all instructions indicated in every activity.

• Answer all questions independently and honestly.

• Write all your answers on a sheet of paper.

• Be sure to compare your answers to the KEY TO CORRECTIONS only after you have answered the given tasks.

• If you have questions or clarifications ask your teacher.

Purpose of Strategic Intervention Material (SIM)

This learning package is intended to supplement your

classroom learning while working independently . The activities

and exercises will widen your understanding of the different

concepts you should learn.

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Honey, I

shrunk the

kids !!!

Title Card

Topic: SUM OF INTERIOR

ANGLES OF POLYGON

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Do you want to know

how the kids got

shrunk ?

Are you kind enough

to help them regain

their normal self ?

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Thank you. I know

you are more than

willing to help.

Sit tight and let’s try to do

the following activities so

that we can unfold their

story.

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Polygon No. of Sides No. of

Triangles

Sum of

Interior

Angles

Triangle

Fill up the table as you follow the instructions:

R

P

R 1

2

3 S

S 1 2 3

R

N M

S 1

2 3

N M

P

P Activity 2

Guide Card

• Do this paper-folding activity using a cutout of a triangle.

• Name the triangle RPS and label the corresponding ∠1,

∠ 2, and ∠ 3 as shown in the figure.

• Fold the triangle so that the point P lies on RS forming a

trapezoid RNMS.

• Fold again so that the vertices R and S meet at point P.

• Determine the sum of the measure of the marked angles

1, 2, and 3.

• Verify your answer by using a protractor.

• Therefore, the sum of the measure of the interior angles of

any triangle is _____ .

Activity 1

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Polygon No. of Sides No. of

Triangles

Sum of

Interior

Angles

Triangle 3 1 1800

Quadrilateral

A D

O R

• Draw all possible diagonals from one

vertex. (e.g. from vertex A)

How many diagonals are possible?

From that possible diagonal/s, how many

triangles are formed?

Take note that the sum of the interior

angles of a triangle is 180º.

The measure of angles 1 + 2 + 3 = 1800

Activity 3

An apple

helps you to

concentrate.

1

2

3

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Polygon No. of Sides No. of

Triangles

Sum of

Interior

Angles

Triangle 3 1 1800

Quadrilateral 4 2 3600

Pentagon

P

D

R

E

O

• Draw all possible diagonals

from one vertex. (e.g. vertex E)

How many diagonals are

possible?

From that possible diagonal/s,

how many triangles are formed?

A D

O R

Since there are two triangles formed, therefore

the sum of the interior angles of a quadrilateral is

3600. Hence, 2(1800)=3600.

Activity 4

I’m an angel

in disguise. I

can help you.

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P

D

R

E

O Therefore, the measure of angles

P+E+D+R+O=5400.

Oh my God !

Now I know.

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Polygon No. of Sides No. of

Triangles

Sum of Interior

Angles

Triangle 3 1 1(1800)=1800

Quadrilateral 4 2 2(1800)=3600

Pentagon 5 3 3(1800)=5400

Hexagon

Heptagon

Octagon

Nonagon

n - gon n n - 2

To check your

answer go to

page 18

The first 3 steps has already

done for you. Follow the same

procedure to complete the

table.

Activity 5

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The couple Poly and Gonny have five nice but

smart kids namely, Trigie, Quadie, Pengie, Hexie, and

Heptie. Mr. Poly is working on an experiment so he

prohibits his siblings to enter a room, where he keeps a

machine which he hopes can transform bigger objects to

smaller once or vice-versa. The kids are so eager and

curious to see the machine which for them can do

magic.

One day, when Mr. Poly is at work and Mrs.

Gonny goes to market, the kids agreed to enter the room

to satisfy their curiosity. Later, the mother came. Finding

the kids nowhere, she proceeded to the laboratory room

and accidentally push a button. A spark of bright light

suddenly appeared. Mrs. Gonny almost lost her

consciousness and shouted “Honey, I shrunk the kids.”

To help the kids regain their normal size you need to

answer the subsequent questions appropriately. For

every correct answer one of the kids will grow back

to its normal size.

The Story Behind…

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1. Find the sum of the interior angles of a 32-gon.

4. The sum of the measure of the interior angles of a polygon is

known to be between 2100 and 2200. How many sides does the

polygon have?

5. In a pentagon PQRST, the measure of angle P is 600, angle

Q is 1300,angle S and T are each 3 times as large as angle R.

Find the measure of angle R, S, and T.

ACTIVITY CARD

To check your

answer go to

page 19

2. The face of a honeycomb consist of interlocking

regular hexagon. What is the measure of each angle of

these hexagons?

3. A soldier’s badge is in the form of a pentagon

with 3 right angles. The other two angles are

congruent. Find their measure.

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Congratulations !

You will receive a

reward for your

help.

To claim your

prize you must

proceed to the

next activity.

Just turn to

next page.

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ASSESSMENT CARD Solve the ff. problems. Write the

letter of the correct answer in each

box at the bottom that contains the

item number.

1. Sum of interior angles of undecagon.

2. Numbers of triangles formed from just

one vertex of 13-gon.

3. Size of each angle of a regular

decagon.

4. No. of sides of n-gon with the sum of

the interior angles 9000.

5. Sum of interior angles of a 30-gon.

6. The no. of sides of a polygon with

1560 each angle.

7. Sum of the interior angles of a

polygon with 1600 each angle.

L 11

S 24

G 15

P 7

F 144

D 5040

R 12

O 2880

T 1620

4 7 1 7 3 6 7 2 5

To check your

answer go to

page 20

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ENRICHMENT CARD

1. Find the sum of the interior angles of

the given polygon if the polygon can be

bisected.

2. Given: ABCDE is a regular pentagon.

Find: a.) the sum of the measure of

angle P, Q, R, S, T.

b.) the measure of each

angle in letter a.

B C

D

F

E

A

D

C

B

A

E

T

S

R

Q P To check your

answer go to

page 21

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http://www.youtube.com/watch?v=JtPK8XezY

PM&feature=related

http://www.youtube.com/watch?v=ZaSjlF4y

BRg&feature=relmfu

http://www.cliffsnotes.com/study_guide/Angle-

Sum-of-Polygons.topicArticleId-18851,articleId-

18794.html

http://www.mathwarehouse.com/geometry/poly

gon/

REFERENCE CARD

Polygons, Geometry (Prentice Hall)

by Bass, Hall, Johnson,Wood, pp.

68-72

Polygons, Geometry by Miftlin, pp.

101-105

Angle Measure of a Triangle,

Geometry by Bernabe, pp. 19-20

Related Topics:

Angle Sum Theorem, Mathematics

(Prentice Hall) by Bass, Charles,

Johnson, Kennedy, pp. 145-150

Polygons, Laidlaw Geometry by Travers,

Dalton, Layton, pp. 460-465

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KEY TO CORRECTIONS ANSWER CARD

Polygon No. of Sides No. of

Triangles

Sum of

Interior

Angles

Triangle 3 1 1(1800)=1800

Quadrilateral 4 2 2(1800)=3600

Pentagon 5 3 3(1800)=5400

Hexagon 6 4 4(1800)=7200

Heptagon 7 5 5(1800)=9000

Octagon 8 6 6(1800)=10800

Nonagon 9 7 7(1800)=12600

n - gon n n - 2 (n – 2)1800

ACTIVITY 5

Brilliant Perfect Score

If you get …

10 - 12

7 - 9

6 and below Start all over

again.

Note: If you are not yet satisfied with your work, you can always go back.

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ACTIVITY CARD

1. 54000

2. 1200

3. 1350

4. 14

5. angle R = 500,

angle S=1500,

angle T=1500

KEY TO CORRECTIONS ANSWER CARD

Perfect Score

5 - 6

4

3 and below Start all over

again.

If you get …

Note: If you are not yet satisfied with your work, you can always go back.

Brilliant

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ASSESSMENT CARD

POT OF GOLD (7 points)

KEY TO CORRECTIONS ANSWER CARD

Start all over

again.

If you get …

Note: If you are not yet satisfied with your work, you can always go back.

Brilliant Perfect Score

5 - 6

4

3 and below

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KEY TO CORRECTIONS ANSWER CARD

Start all over

again.

If you get …

Note: If you are not yet satisfied with your work, you can always go back.

Brilliant Perfect Score

2

0 - 1

ENRICHMENT CARD

1. 7200

2. a.) 1800

b.) 360