TRIANGLE

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Media and Video
BASE COMPETENCE
CLASS ROOM ACT
PROBLEM
By Darto, SMP N 4 Pakem
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BASE COMPETENCE
6.1 Indentify the property of triangle based on
their sides and angles
6.2 Drawing a triangle, altitude, bisector,
Median and axis on triangle
6.3 Count the perimeter and the area of
triangle, and how to use in problem solving
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CLASS ROOM ACT
THE GENERAL PROPERTIES OF TRIANGLE
THE KINDS OF TRIANGLE
HOW TO DRAW
MEASUREMENT
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THE GENERAL PROPERTIES OF TRIANGLE
1. Has 3 angles
That are called inner angles
Problem -1
2. Has 3 sides
The longest side
less than the sum of both side another
Problem -2
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Angles in a Triangles
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PROBLEM -1

• 1.Determine the angle in the triangle isnt known
  yet if given two angle
• a. 23, 67,
• b. 37, 84,
• 2. Determine the value of x
• if the angle in the triangle are
• a. 4x, 5x6, 9x -6
• b. 2x, 3x, 5x

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EXERCISES-1
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EXERCISES-2
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Conclusion
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Problem-2
1. Tentukan manakah 3 pasang segmen garis yang
dapat dibuat segitiga
Pasangan seg. Garis(cm) Cek, please Cek, please
Pasangan seg. Garis(cm) Bisa Tidak
4, 7, 8
5, 6, 10
7, 15, 6
8, 10, 19
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The sum of the lengths of any two sides of a
triangle is greater than the third side.
5
12
15
515 gt12 or 20gt12
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The sum of the lengths of any two sides of a
triangle is greater than the third side.
5
12
15
1215 gt5 or 27gt5
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The sum of the lengths of any two sides of a
triangle is greater than the third side.
5
12
15
512 gt15 or 17gt15
515 gt12 or 20gt12
1215 gt5 or 27gt5
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STANDARD 6
The measures of two sides of a triangle are 15
and 8. Between what two numbers is the third side.
X
15X gt 8
8X gt 15
158 gt X
The third side will be any value between 7 and 23.
23 gt X
8X gt 15
15X gt 8
-8 -8
X lt 23
-15 -15
X gt 7
X gt -7
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If a triangle has sides of measure x, x4,
3x-5, find all possible values of x
(3X-5) X gt (X4 )
4X 5 gt X 4
-X -X
3X 5 gt 4
5 5
3X gt 9
(X4)(3X-5) gt X
(X4 )X gt (3X-5)
X gt 3
4X -1 gtX
2X 4 gt 3X-5
-4X -4X
-2X -2X
4 gt X-5
-1 gt-3X
5 5
9 gt X
.3 ltX
X lt 9
Xgt.3
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If one side of a triangle is the longest then
B
A
C
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If one side of a triangle is the longest then
B
A
C
The opposite angle to this side is the largest
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B
A
C
And the angle opposite to the shortest side
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The sum of the lengths of any two sides of a
triangle is greater than the third side.
5
12
15
512 gt15 or 17gt15
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1. Do you remember about acute angle
2. Observe the size all of angle in the triangle
   bellow

3. What did you get
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1. Do you remember about obtuse angle 2. Observe
the size all of angle in the triangle bellow
3. What did you get
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THE KINDS OF TRIANGLE

• BASE ON THE SIZE ANGLE
• III. 1. Do you remember about right angle
• 2. Observe the size all of angle in the triangle
  bellow

3. What did you get
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Problem -3

• Determine the kind of triangle bellow if
• 1. The angle are 65, 75, 80
• 2. The angle are 25, 60, 95
• 3. The angle are 54, 56, 70
• 4. Two angle are 73, 34,
• 5. The proportion of angle is 3 4 5
• 6. The proportion of angle is 2 3 4
• 7. The angle is 6x, 2x 3, 4x 9

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PROBLEM-3
determine the value of x
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THE KINDS OF TRIANGLE

• BASE ON THE LENGTH SIDE
• I. 1. Observe the length of all side in the
  triangle bellow

2. What did you get
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THE KINDS OF TRIANGLE

• BASE ON THE LENGTH SIDE
• II. 1. Observe the length of all side in the
  triangle bellow

2. What did you get
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THE KINDS OF TRIANGLE

• BASE ON THE LENGTH SIDE
• III. 1. Observe the length of all side in the
  triangle bellow

2. What did you get
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RIGHT TRIANGLES

• 1. Recall Pythagorean theorem
• 2. Indentify The kinds of Triangle by using
  Pythagorean theorem
• 3. The kinds of Triple Pythagorean number and its
  expectation
• 4. The specific side proportion of right triangle

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30-60-90 TRIANGLE
PROBLEM 1
PROBLEM 2
PROBLEM 3
45-45-90 TRIANGLE
PROBLEM 4
PROBLEM 5
PROBLEM 6
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60
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1. An equilateral triangle is also equiangular,
all angles are the same.
2. Lets draw an Altitude from one of the
vertices. Which is also a Median and Angle
bisector.
3. The bisected side is divided into two equal
segments and the bisected angle has now two 30
equal angles.
How is the right angle that was formed? Click to
find out
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z
-1 -1
4. The triangle is divided into 2 right angles
with acute angles of 30 and 60
5. Lets draw the top triangle and label the
unknown side as z.
6. Lets apply the Pythagorean Theorem to find
the unknown side.
Can we generalize this result for all 30-60-90
right triangles? Click to find out
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7. Is this true for a triangle that is twice as
big?
8. Is this true for a triangle that is half the
original size?
9. What about a triangle that is s times bigger
or Smaller?
Click to find out
37
60
2
30
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Find the values of the variables. Round your
answers to the nearest hundredth.
y
2x 50
30
2x 50
x
2 2
50
60
x 25
Is this 30-60-90?
90-3060
Then we know that
OR
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Find the values of the variables. Round your
answers to the nearest unit.
2x y
30
y
90
.
OR
60
x
x
Is this a 30-60-90?
90-6030
OR
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Find the values of the variables. Find the exact
answer.
x
2x y
60
y
.
30
30
x
Is this a 30-60-90?
90-6030
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1. Lets draw a diagonal for the square above.
The diagonal bisects the right angles of the
square.
What kind of right triangles are form? Click to
find out
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y
2. The triangles are 45-45-90
3. Lets draw the bottom triangle and label the
hypotenuse as y
4. Lets apply the Pythagorean Theorem to find
the hypotenuse.
Can we generalize our findings? Click to find out
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s
s
5. Lets draw a triangle half the size of the
original.
s
6. Lets draw a triangle one and a half the size
of the original.
7. Lets draw a triangle S times the size of the
original.
Click to see our findings
44
45
s
s
45
s
45
Find the values of the variables. Round your
answers to the nearest tenth.
45
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x
If y x
.
then
45
OR
x
y
Is this a 45-45-90?
90-4545
OR
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Find the values of the variables. Give an exact
answer.
45
42
x
If y x
.
then
45
x
y
Is this a 45-45-90?
90-4545
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Find the values of the variables. Give the exact
answer.
x 21
45
y
x
45
21
Is this a 45-45-90?
90-4545