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FOURTH GRADE / GEOMETRY 2.1 / TRIANGLES, SIMPLE POLYGONS and CIRCLES

MATHEMATICS IS EASY. PROVIDED THAT ONE WORKS ENOUGH .
ENOUGH IS SKILL DEPENDENT, HAVE TO FIND "ENOUGH" FOR YOUR SIZE.

   PLANE SHAPES WE WILL INVESTIGATE ARE
 ♦ 
TRIANGLES, POLYGONS and CIRCLES
 ♦ A TRIANGLE IS ALSO A POLYGON BUT IT IS THE GATE TO THE WORLD OF POLYGONS AND WE TREAT IT SEPARATELY.

THERE ARE TWO GOLDEN RULES:
1. THE SUM OF INNER ANGLES OF A TRIANGLE IS 180 DEGREES. FOR POLYGONS COUNT THE NUMBER OF TRIANGLES WITHIN.
2. A CLOSED CONVEX SHAPE ALWAYS HAS , FOR THE SUM OF ITS EXTERIOR ANGLES, 360 DEGREES.
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1. How are triangles classified as to sides ?

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In case of need for tips get the cursor on "y" or for help click at "ry1/2" .
RY1 RY2



a) equal sided, different sided and non equal sided
b) equal sided and non equal sided
c) scalene, isosceles and equilateral
d) scalene and isosceles


If all sides different scalene .
if two sides equal isosceles .
if all sides equal equilateral .
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2. How are triangles classified as to angles ?

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In case of need for tips get the cursor on "y" or for help click at "ry1/2" .

RY1 RY2



a) equal angled and non equal angled
b) acute, right and obtuse
c) acute and right
d) oblique, acute and obtuse
ıf all angles acute, acute triangle .
One angle right or obtuse, then right or obtuse triangle.
Some include equilateral but not generally accepted.
3. Which choice gives all parts of a triangle ?

a) sides
b) sides and angles
c) sides, angles and vertexes
d) sides angles and vertices
Vertices are not considered as parts, they are dimensionless
4. What is a triangle without any right angle called ?

a) oblique
b) acute
c) obtuse
d) not right
ob.... .
5. What kind of triangle is half of a square ?

a) right
b) rechtangled
c) isosceles
d) none or right isosceles
Half of a square is not necessarily a triangle .
6. Which of the followings should be true for the sides of a triangle ? (Triangle Inequality)

a) The sum of squares of two sides is equal to the 3rd side.
b) The sum of squares of two sides is equal to the square of the 3rd side.
c) The sum of two sides is less than the third side.
d) The sum of two sides is greater than the third side.
Triangle inequality is pretty important .
7. Equilateral triangle is our first regular polygon, the simplest with 3 sides. Of course regular polygons are important with all inner angles equal and all sides equal. Ultimateley they happen to be a circle and they all fit in a circle.
What should be the measure of an interior angle (in degrees) of an equilateral triangle ?

!


a) 60
b) 80
c) 90
d) 45
Since the sum of inner angles of a triangle is 180 degrees, ... .
8. If the red segments are bisectors of the angles, what kind of tringle should AOC be ?

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a) acute
b) equal
c) equilateral
d) isosceles
Isosceles triangles do have two of their interior angles equal.
9. Which angle of the isosceles triangle AOC is usually considered as the vertex angle for this kind ?

!


a) ∠OAC
b) ∠AOC
c) ∠OCA
d) ∠BAC


In isosceles triangles the inequal angle is usually considered as the vertex angle. The side opposite vertex angle is the base and base angles are equal .
10. The triangle ADC is a right triangle . What is the side b called ?

!


a) longest side
b) right angle side
c) hypotenuse
d) opposite side
In right triangles the sides including the right angle are called legs and the (longest) side opposite the right angle is called hypotenuse .
11. Considering the right triangle ABC, the ∠B is included by BC and the .... ?

!


a) opposite side
b) hypotenuse
c) CA
d) DA
The ∠B is included by the sides AB and BC .
The side AB is included by ∠A and ∠B .
12. Considering triangles ABC and ABD of the figure of q.11 , the side AD is ... .

a) shared
b) common
c) adjacent
d) equal
When a side of a triangle is also a side of another triangle we say the side is common .
13. The regular quadrilateral (polygon with 4 sides) is called a ... . ?

a) square
b) rhombus
c) tetrahedral
d) polygon
Rhombus is an equilateral parallelogram, including the square as a special case. That is, if the angles are also equal, a rhombus is a square.
14. How big is the measure of the ∠CDB ?

!
a) 60°
b) 40°
c) 55°
d) 45°
The triangle isosceles and the vertex angle is 90° .
15. One side of the square shown in the figure has a length of 4 units.
How many squares of unit area exists in the square shown in the figure ?

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a) 12
b) 16
c) 8
d) 20
The column left has 4 unit squares and there are ... columns .
16. ABCD is a rectangle. How big is the area of the yellowish region in terms of legs ?

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a) half of leg1 (base) x leg2 (height)
b) leg1 (base) x leg2 (height)
c) leg1 (base) x leg2 (height)x2
d) leg1 (base) x leg2 (height)x 2/3
One of the legs is the base of the triangle and the other is the height.
17. Which choice gives the area of the rectangle ABCD ?

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a) 12 cm2
b) 16 cm2
c) 15 cm2
d) 18 cm2
By rectangles the area = sideshort x sidelong .
18. Both the square and the rectangle in the figure below have equal perimeters. Their aras are different though.
Which of the followings may be considered as a plausible explanation ?

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The area of convex polygons of same perimeters increases as
I- the number of the sides increases,
II- they get bigger and
III- the the shape gets regular.

a) only I
b) only II
c) only III
d) I and III
Perimeter is here a restriction on which the question is based .
19. The square is the regular quadrilateral. As we give up the equality of the angles we get ... . ?

a) parallelogram
b) rectangle
c) rhombus
d) pentagon
The sides are kept equal .
20. The square is the regular quadrilateral. As we give up the equality of the sides we get ... .

a) another square
b) rhombus
c) rectangle
d) parallelogram
all angles are still equal .
21. The rectangle has all angles equal. If we soften the rule and restrict ourselves to the equality of opposite (non adjacent) angles we get ... .

a) parallelogram
b) trapezoid
c) trapezium
d) rhombic
Since the opposite angles are equal, opposite sides should be parallel.
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22. What will be the sum of interior angles of a convex heptagon (polygon with 7 sides) ?

In case of need for tips get the cursor on "y" or for help click at "ry1/2".

RY1 RY2



a) 900°
b) 800°
c) 720°
d) 600°


Draw all possible triangles of 7 vertices, sum the angles .In general there will be "number of sides - 2" triangles each having a sum of 180°
23. A convex polygon is a polygon with no ... angle .



a) interior
b) exterior
c) reflex
d) acute
A reflex angle is greater than 180º and less than 360º.
24. What is the sum of outer angles of a convex polygon ?

a) 180°
b) 720°
c) 180° x no. of sides
d) 360°
A perigon (or a revolution) is an angle that equals exactly 360º and is completed with completion of a closed convex figure.
25. A polygon whose boundary does not cross itself is called a ... polygon .

a) complex
b) oblique
c) normal
d) simple
Convex: any line drawn through the polygon (and not tangent to an edge or corner) meets its boundary exactly twice .
Simple: the boundary of the polygon does not cross itself. All convex polygons are simple.
This is the feedback!

THANK YOU FOR YOUR VISIT; HOPE WE COULD BE OF USE.
FOR MUTUAL BENEFIT YOU MAY USE OUR FORUM.
© 2011 , Ä°smail GERMAN. ALL RIGHTS RESERVED
PLEASE PREFER GIVING LINK IF THAT SUFFICES

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