STRATEGIC
INTERVENTION
MATERIAL

1

RIZAL HIGH SCHOOL
SY 2011 - 2012

Prepared by:
Asakil, Flordeliza V.
Casumbal, Epifania J.

Dela Cruz, Lorena O.
Pagulayan, Rowena H.
Reluba, Ma. Theresa C.

Unida, Francisca R.
2

2

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.

How to use this Strategic Intervention Material (SIM)?
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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.
3

Honey, I shrunk the kids !!!

Title Card

Topic:

SUM OF INTERIOR
ANGLES OF POLYGON

4

Are you kind enough to help them regain their normal self ?
Do you want to know how the kids got shrunk ?

5

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. 6

Guide Card

P
2

Activity 1

1

• 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.

S

R
N

• 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.

3

M
2

1

R

3

S

P

• Determine the sum of the measure of the marked angles
1, 2, and 3.
• Verify your answer by using a protractor.

N

• Therefore, the sum of the measure of the interior angles of any triangle is _____ .

M
1 2 3

R

S

P

Activity 2

Fill up the table as you follow the instructions:
Polygon

Triangle

No. of Sides

No. of
Triangles

Sum of
Interior
Angles
7

2
1

The measure of angles 1 + 2 + 3 = 1800
3
A

D

Activity 3
• Draw all possible diagonals from one vertex. (e.g. from vertex A)
How many diagonals are possible?

R

O

From that possible diagonal/s, how many triangles are formed?
Take note that the sum of the interior angles of a triangle is 180º.
Polygon

Triangle
Quadrilateral

No. of Sides

3

No. of
Triangles

Sum of
Interior
Angles

1

1800

An apple helps you to concentrate. 8

A

D

Since there are two triangles formed, therefore the sum of the interior angles of a quadrilateral is
3600. Hence, 2(1800)=3600.
R

P

Activity 4

E

O

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?

D

R

Polygon

No. of Sides

No. of
Triangles

Sum of
Interior
Angles

Triangle

3

1

1800

Quadrilateral

4

2

3600

Pentagon

I’m an angel in disguise. I can help you.
9

P

Therefore, the measure of angles
P+E+D+R+O=5400.

E

D

O
R

Oh my God !
Now I know.

10

Activity 5
The first 3 steps has already done for you. Follow the same procedure to complete the table. 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

n

n-2

Hexagon
Heptagon
Octagon
Nonagon
n - gon

To check your answer go to page 18

11

The Story Behind…
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.

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ACTIVITY CARD

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

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.
To check your answer go to page 19

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Congratulations !
You will receive a reward for your help. Just turn to next page.

To claim your prize you must proceed to the next activity.

14

Solve the ff. problems. Write the letter of the correct answer in each box at the bottom that contains the item number.

ASSESSMENT CARD

1. Sum of interior angles of undecagon.

L

11

2. Numbers of triangles formed from just one vertex of 13-gon.

S

24

G

15

P

7

4. No. of sides of n-gon with the sum of the interior angles 9000.

F

144

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

D

5040

6. The no. of sides of a polygon with
1560 each angle.

R

12

3. Size of each angle of a regular decagon. O

4

7

1

7

3

6

7

2880

T

7. Sum of the interior angles of a polygon with 1600 each angle.

To check your answer go to page 20

1620

2

5
15

ENRICHMENT CARD
A

F

1. Find the sum of the interior angles of the given polygon if the polygon can be bisected. E

D

C

B

B

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.

P

A

Q

T

C

R

To check your answer go to page 21

S
E

D

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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

http://www.cliffsnotes.com/study_guide/AngleSum-of-Polygons.topicArticleId-18851,articleId18794.html http://www.youtube.com/watch?v=JtPK8XezY PM&feature=related http://www.mathwarehouse.com/geometry/poly gon/ http://www.youtube.com/watch?v=ZaSjlF4y BRg&feature=relmfu
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

If you get …

ACTIVITY 5
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

9

7

n

n-2

(n – 2)1800

10 - 12

7-9

7(1800)=12600

n - gon

Brilliant

6(1800)=10800

Nonagon

Perfect Score

6 and below

Start all over again. 18

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

KEY TO CORRECTIONS

ANSWER CARD

If you get …

ACTIVITY CARD

Perfect Score

Brilliant

1. 54000
2. 1200

5-6

3. 1350
4. 14

4

5. angle R = 500, angle S=1500, angle T=1500

3 and below

Start all over again. 19

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

ANSWER CARD

KEY TO CORRECTIONS
If you get …

ASSESSMENT CARD

Perfect Score

Brilliant

POT OF GOLD (7 points)
5-6

4

3 and below

Start all over again. 20

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

KEY TO CORRECTIONS

ANSWER CARD

If you get …

ENRICHMENT CARD

Perfect Score

Brilliant

1. 7200
2. a.) 1800

2

b.) 360
0-1

Start all over again. 21

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