Math Quiz Pib - Proofs And Symmetry

1) What's the angle sum of a triangle?

The angle sum of a triangle is always 180 degrees. This is a fundamental property of triangles in Euclidean geometry. The sum of the three interior angles of any triangle will always be equal to 180 degrees.

Explanation

The angle sum of a triangle is always 180 degrees. This is a fundamental property of triangles in Euclidean geometry. The sum of the three interior angles of any triangle will always be equal to 180 degrees.

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2)

How many degrees are each angle? Match the following alternatives by the correct angle:

a)

b)

c)

d)

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3)

Match the following triangles:

a)

b)

c)

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4)

"The triangle is right angled"...True or false?

True

False

Explanation

5) What's the angle sum of a quadrilateral? (fyrhörning)

The angle sum of a quadrilateral is always 360 degrees. This is because a quadrilateral has four angles, and the sum of the interior angles of any polygon is given by the formula (n-2) * 180, where n is the number of sides. In the case of a quadrilateral, n = 4, so the sum of the interior angles is (4-2) * 180 = 2 * 180 = 360 degrees.

Explanation

The angle sum of a quadrilateral is always 360 degrees. This is because a quadrilateral has four angles, and the sum of the interior angles of any polygon is given by the formula (n-2) * 180, where n is the number of sides. In the case of a quadrilateral, n = 4, so the sum of the interior angles is (4-2) * 180 = 2 * 180 = 360 degrees.

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6)

Match the following angles:

a)

b)

c)

d)

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8)

What is x? (How many degrees)

The side angle to x is 180-150=30 (the angle sum is 180)
x+30 = 180 (side angles are 180)
x=150

Explanation

The side angle to x is 180-150=30 (the angle sum is 180)
x+30 = 180 (side angles are 180)
x=150

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9) Which of the following alternatives are true about equilateral triangles? (liksidiga trianglar) (More than one alternative can be correct.)

In equilateral triangles, two sides are equal in length

In equilateral triangles, all sides are equal in length

In equilateral triangles, the two base angles are equal (basvinklarna är lika)

In equilateral triangles, all angles are equal

In equilateral triangles, all sides are equal in length because the definition of an equilateral triangle is a triangle with all sides of equal length. Additionally, in equilateral triangles, all angles are equal because the sum of the angles in any triangle is always 180 degrees, and since all sides are equal, all angles must also be equal.

Explanation

In equilateral triangles, all sides are equal in length because the definition of an equilateral triangle is a triangle with all sides of equal length. Additionally, in equilateral triangles, all angles are equal because the sum of the angles in any triangle is always 180 degrees, and since all sides are equal, all angles must also be equal.

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11)

How many degrees is angle x?

The triangle is isosceles, so the base angles are equal.

2x + 40 = 180 (angle sum)
2 x =140
x=70

Explanation

The triangle is isosceles, so the base angles are equal.

2x + 40 = 180 (angle sum)
2 x =140
x=70

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12) Which of the following alternatives are true about isosceles triangles? (likbenta trianglar) (More than one alternative can be correct.)

In isosceles triangles, two sides are equal in length

In isosceles triangles, all sides are equal in length

In isosceles triangles, the two base angles are equal (basvinklarna är lika)

In isosceles triangles, all angles are equal

In isosceles triangles, two sides are equal in length, and the two base angles are equal. However, not all sides are equal in length and not all angles are equal in isosceles triangles.

Explanation

In isosceles triangles, two sides are equal in length, and the two base angles are equal. However, not all sides are equal in length and not all angles are equal in isosceles triangles.

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13) Which of the following alternatives is true about theorems?

A theorem is the same as a statement

A theorem is the same as a definition

A theorem is based on experiments and observations

A theorem is a statement which has been mathimatically proven

A theorem is a starting point of reasoning

A theorem is a statement which has been mathematically proven. Theorems are not the same as definitions, as definitions provide the meaning of terms or concepts. Theorems are also not based on experiments and observations, as they are derived through logical reasoning and mathematical proof. Theorems serve as important results in mathematics, providing a foundation for further mathematical developments and applications.

Explanation

A theorem is a statement which has been mathematically proven. Theorems are not the same as definitions, as definitions provide the meaning of terms or concepts. Theorems are also not based on experiments and observations, as they are derived through logical reasoning and mathematical proof. Theorems serve as important results in mathematics, providing a foundation for further mathematical developments and applications.

14) Which of the following formulas is used to calculate the scale?

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Explanation

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15)

How many lines of symmetry does each traffic sign have if you take the following into consideration: outer shape, the text, colour and the content? OBS! Type your answer like this: Ex: A3 B2 C5 D0

Explanation

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16) On a map with scale 1:350 000 is the distance between two cities 5 cm. How many kilometers is the distance in real life?

1 cm on the map is 350 000 cm in real life.
5 cm on the map is 5x350 000 cm in real life

5x350 000 = 1 750 000cm
1 750 000 / 100 = 17500 m
17500 / 1000 = 17.5 km

ANS: 17.5

Explanation

1 cm on the map is 350 000 cm in real life.
5 cm on the map is 5x350 000 cm in real life

5x350 000 = 1 750 000cm
1 750 000 / 100 = 17500 m
17500 / 1000 = 17.5 km

ANS: 17.5

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17) What is missing in the proof?

Triangle ABC is equilateral. Show that the angle DAC = 30 degrees

1.

2.

3.

4.

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18)

What relationship do the angles u and v have in each picture? What are the angles called?

a)

b)

c)

d)

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19)

How many lines of symmetry does each traffic sign have if you take the following into consideration: only the outer shape of the signs? OBS! Type your answer like this: Ex: A3 Binfinite C5 D0

Explanation

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20)

What is v in each figure? Match the following alternatives:

a)

b)

c)

d)

a) The sum of side angles is 180 degrees, and 180-100=80
b)Vertical angles are equal (vertikalvinklar)
c) Corresponding angles are equal (likbelägna vinklar)
d) Alternate angles are equal (alternativinklar)

Explanation

a) The sum of side angles is 180 degrees, and 180-100=80
b)Vertical angles are equal (vertikalvinklar)
c) Corresponding angles are equal (likbelägna vinklar)
d) Alternate angles are equal (alternativinklar)

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21) Which scales indicate a reduction (förminskning)?

1:4000

2:5

6:1

15:16

20000:1

If it's a reduction we have a smaller number in front of a larger number.

Explanation

If it's a reduction we have a smaller number in front of a larger number.

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22)

What is the line k called? (in english or swedish)

The line k is called a bisector or bisektris, which refers to a line that divides an angle or a line segment into two equal parts.

Explanation

The line k is called a bisector or bisektris, which refers to a line that divides an angle or a line segment into two equal parts.

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23)

By how many degrees is each figure rotational symmetric? (Hur många grader kan man rotera figuren innan den överlappar sin ursprungliga form?) Match the following alternatives:

A

B

C

D

Imagine that you are standing at the top of the figure and watching it. Then you start moving counter clockwise along the figure. How many degrees do you have to move until the figure looks exactly the same as it did from your original view? (The eye in the picture symbolises you watching the figure...)

Explanation

Imagine that you are standing at the top of the figure and watching it. Then you start moving counter clockwise along the figure. How many degrees do you have to move until the figure looks exactly the same as it did from your original view? (The eye in the picture symbolises you watching the figure...)

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24) Which of the following implications are equivalent? (Which of the following

can be replaced by

?)

An Italian is also a citizen of EU
An octopus can also have eight legs
If all angles are equal then the triangle is equilateral
2x8+3=19
A negative number is always less than 0
An acute angle could be anything between 0 and 90, 30 for example.
The radius is always half the diameter, and 10/2=5

Explanation

An Italian is also a citizen of EU
An octopus can also have eight legs
If all angles are equal then the triangle is equilateral
2x8+3=19
A negative number is always less than 0
An acute angle could be anything between 0 and 90, 30 for example.
The radius is always half the diameter, and 10/2=5

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25)

In which triangles can Pythagoras' theorem be used to calculate the unknown length?

A)

B)

C)

D)

Pythagoras' theorem can be used only in right angled triangles (rätvinkliga). Triangles a) b) and c) are right angled.

(Triangle c) is right angled since it is an isosceles triangle with one base angle 45 degrees, and then the other base angle must also be 45 degrees. 45+45=90 and 180-90, which means the third angle in triangle c) is 90 degrees, hence the triangle is right angled!)

Explanation

Pythagoras' theorem can be used only in right angled triangles (rätvinkliga). Triangles a) b) and c) are right angled.

(Triangle c) is right angled since it is an isosceles triangle with one base angle 45 degrees, and then the other base angle must also be 45 degrees. 45+45=90 and 180-90, which means the third angle in triangle c) is 90 degrees, hence the triangle is right angled!)

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26) Which of the following implications are true?

It could snow in June
Equilateral triangles have equal angles
There are rich people who are very sad
4+16=20
A square is also a rectangle (all angles are 90 degrees)

Explanation

It could snow in June
Equilateral triangles have equal angles
There are rich people who are very sad
4+16=20
A square is also a rectangle (all angles are 90 degrees)

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