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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.
What's the angle sum of a quadrilateral? (fyrhörning)
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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3.
Which of the following alternatives are true about isosceles triangles? (likbenta trianglar)
(More than one alternative can be correct.)
A.
In isosceles triangles, two sides are equal in length
B.
In isosceles triangles, all sides are equal in length
C.
In isosceles triangles, the two base angles are equal (basvinklarna är lika)
D.
In isosceles triangles, all angles are equal
Correct Answer(s) A. In isosceles triangles, two sides are equal in length C. In isosceles triangles, the two base angles are equal (basvinklarna är lika)
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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4.
Which of the following alternatives are true about equilateral triangles? (liksidiga trianglar)
(More than one alternative can be correct.)
A.
In equilateral triangles, two sides are equal in length
B.
In equilateral triangles, all sides are equal in length
C.
In equilateral triangles, the two base angles are equal (basvinklarna är lika)
D.
In equilateral triangles, all angles are equal
Correct Answer(s) B. In equilateral triangles, all sides are equal in length D. In equilateral triangles, all angles are 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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5.
What is x? (How many degrees)
Correct Answer(s) 150 degrees 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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6.
In which triangles can Pythagoras' theorem be used to calculate the unknown length?
A.
A)
B.
B)
C.
C)
D.
D)
Correct Answer(s) A. A) B. B) C. C)
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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7.
Calculate the unknown length.
Correct Answer(s) 3
Explanation Use Pythagoras' theorem:
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8.
What is the line k called?
(in english or swedish)
Correct Answer(s) bisector bisektris
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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9.
How many degrees is angle x?
Correct Answer(s) 110
Explanation The angle sum of a triangle is 180 degrees, so x = 180-30-50 = 110
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10.
How many degrees is angle x?
Correct Answer(s) 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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11.
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
Correct Answer(s) A2 B8 C3 Dinfinite
12.
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
Correct Answer(s) A1 B0 C3 D1
13.
Which scales indicate a reduction (förminskning)?
A.
1:4000
B.
2:5
C.
6:1
D.
15:16
E.
20000:1
Correct Answer(s) A. 1:4000 B. 2:5 D. 15:16
Explanation If it's a reduction we have a smaller number in front of a larger number.
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14.
Which of the following formulas is used to calculate the scale?
A.
B.
C.
Correct Answer B.
15.
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?
Correct Answer 17.5 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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16.
Which of the following implications are true?
A.
B.
C.
D.
E.
Correct Answer(s) B. D. E.
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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17.
Which of the following implications are equivalent? (Which of the following can be replaced by ?)
A.
B.
C.
D.
E.
F.
G.
Correct Answer(s) C. D. E. G.
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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18.
Which of the following alternatives is true about theorems?
A.
A theorem is the same as a statement
B.
A theorem is the same as a definition
C.
A theorem is based on experiments and observations
D.
A theorem is a statement which has been mathimatically proven
E.
A theorem is a starting point of reasoning
Correct Answer D. A theorem is a statement which has been mathimatically proven
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.
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19.
"The triangle is right angled"...True or false?
A.
True
B.
False
Correct Answer B. False
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