Colourful Life with Mathematics ^^

Name : Ika Dewi Fitria Maharani
NIM : 11301241009
 
1. Describe the types of the following triangles in term of the measure of their angles.
Page 281 at Marsigit`s book class 1

SOLUTION :
 a. Look at picture 1.a in Page 281 at Marsigit`s book class 1
We can see the triangle that containing exactly one 90 degrees (we can call it right angle). The other two angles must be total exactly 90 degrees.
Example : The other two angles are 45 degrees or the one angle is 60 degrees and the other angle is 30 degrees. It is up to us, but the other two angle must be total exactly 90 degrees
We have to know why it must be total exactly 90 degrees!
Because if we calculate all the angles at triangle, it must be total exactly 180 degrees.
Finally, we call the triangle is right triangle because one of their angles is right.

b. Look at the picture 1.b in Page 281 at Marsigit`s book class 1
We can see the triangle contains one angle that is greater than 90 degrees (we can call it obtuse angle) and the other two angles must be total less than 90 degrees.
Why? Because total of the three angles must be exactly 180 degrees.
Finally, we call the triangle is obtuse triangle because one of the angles is obtuse and the two uf angles are less than 90 degrees.



c. Look at the picture 1.c in Page 281 at Marsigit`s book class 1
We can see the triangle that containing three angles that are all less than 90 degrees or acute angle. So, the triangle we call acute triangle because all three of its angles are acute.
Then if all three of its angles are 60 degrees, we can call the triangle is equilateral triangle.
Now, we can differentiate the triangle by its angles, there are :
 1.Right triangle because one of their angles is right ( 90 degrees)
 2.Obtuse triangle because one of their angles is obtuse ( greater than 90 degrees)
 3.Acute triangle because all three of  its angles are acute ( less than 90 degrees)

2. Consider the following square (Look at picture 2 in Page 281 at Marsigit`s book class 1).
Construct both diagonals of that square, then describe four triangles that you found!
Page 281 at Marsigit`s book class 1

SOLUTION :
First, i will tell about the definition of square. A square is two-dimensional figure with four straight sides, whose four interior angles are 90 degrees or right angle.
Then, i will give the square name, there is ABCD square. So we can make the diagonals at the square ABCD.
But, we have to know too the definition of diagonal!
The diagonal is a straight line inside a shape that goes from one corner to another corner (but not an edge)
Now, we make the diagonal from corner A to corner C. We call it diagonal AC.
Then, we make the diagonal from corner B to corner D. We call it diagonal BD.
Because we make two diagonal so the square now have a point at the center of the square. We give name O to the point.
We can see that diagonal AC and diagonal BD are producing four triangle. But we have to know the definition of triangle. A triangle is a plane figure with three straight sides.
Now, we can find four triangle at the square. There are :
 1. Triangle AOB. It have three straight sides (definition of triangle), there are sides AO,OB and AB .
 2. Triangle BOC. It have three straight sides (definition of triangle), there are sides BO,OC and BC .
 3. Triangle COD. It have three straight sides (definition of triangle), there are sides CO,OD and CD .
 4. Triangle AOD. It have three straight sides (definition of triangle), there are sides AO,OD and AD .
Okay, we have succes find four triangles at the square.

3. Andi bought three pairs of shoes at cost Rp. 225.000,00  totally. What was the price of a pair of shoes?
Page 117 from Marsigit`s book class 1

SOLUTION :
From the question we know :
   a. The total pairs of shoes that Andi bought is three
   b. The total cost that Andi use to buy three pairs of shoes is Rp 225.000,00
If we want to know the price of a pair shoes , we can devide the total cost that Andi use to buy three pairs of shoes with the total pairs of shoes that Andi bought. So we devide Rp 225.000 with three and we get Rp 75.000 for the price of a pair of shoes.

4. The following mentally 5 + (2 + (-3)) = (5 + 2) + (-3) the law of ...
    a. Commutative
    b. Associative
    c. Distributive
    d. The distributive of multiplication to addition
Page 203 from Marsigit`s book class 1

SOLUTION :
We have to know the definition of Commutative, Associative, Distributive and The
distributive of multiplication to addition before try to solve this question.

First, Commutative law if a and b are the integers, then a plus b equal to b plus a
Example : three plus five equal to five plus three equal to eight.
In Mathematics : 3 + 5 = 5 + 3 = 8

Second, Associative law if a, b, and c, are the integers, then ( a plus b) plus c equal to a plus (b plus c).
Example : (one plus two) plus three equal to one plus (two plus three) equal to six.
In Mathematics : (1 + 2) + 3 = 1 + (2 + 3) = 6

Then, Distributive and The distributive of multiplication to addition are not the properties of addition operation.

Okay, now the solution only two, commutative or associative.
From the definition we can conclude that the solution from the question is associative (b).

5. Fill the blank below. Decide the couple of the congruent triangles in the following figure. (Look at picture in Page 19 at Marsigit`s book class 3)
AB = ....
BD = ....
AD = ....
∆ABD congruent ...
Page 19 at Marsigit`s book class 3

SOLUTION :
The picture is ABCD  rectangle, then it have one diagonal (AD diagonal).
First, we must know the definiton of rectangle and diagonal.

 A rectangle is a quadrilateral with two pairs of parallel sides, four right angles, opposite sides equal in length, equal diagonals bisecting one another.

The diagonal is a straight line inside a shape that goes from one corner to another corner (but not an edge)

The diagonal devide the rectangle become have two congruent triangle, there are ABD triangle and ACD triangle (Look at picture in Page 19 at Marsigit`s book class 3). Why the triangle is congruent? Because object that have similar form and size are called congruent object.
Then the requirements for the congruence of two plane figures are If  the corresponding lengths and sizes of angles are equal.
Now we know about the definition of rectangle, diagonal and the congruence of two plane figure so we can solve tjis question. :)
AB = CD (the corresponding lenghts are equal)
BD = AC (the corresponding lenghts are equal)
AD = AD (superimpose into each other so the corresponding lenghts are equal)
∆ABD congruent ∆ACD because they have the corresponding lengths and sizes of angles are equal.
The corresponding lengths :
AB = CD (the corresponding lenghts are equal)
BD = AC (the corresponding lenghts are equal)
AD = AD (superimpose into each other so the corresponding lenghts are equal)
the corresponding sizes of angles :
corner of ABD = corner of ACD = 90 degrees
corner of BAD = corner of CDA = corner of BDA = corner of CAD = 45 degrees
Because if we calculate all the angles at triangle, it must be total exactly 180 degrees and Because if we calculate all the angles at retangle, it must be total exactly 360 degrees. :)