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FOURTH GRADE / GEOMETRY 2.3 / 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.
y
1. ADFE is a rectangle and GC//FA (// means is parallel to). What is the numerical value of |BE| ?

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



a) 20 cm.
b) 10 cm.
c) 12 cm.
d) 17 cm.


GDE is equilateral . For help have a look at ry1
y
2. ADFE is a rectangle and GC//FA (// means is parallel to). What is the numerical value of |GC| ?

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

RY1 RY2



a) 5 cm.
b) 10 cm.
c) 7 cm.
d) 15 cm.
Well, this is one of the simplest examples of similar triangles and ratios of their sides. Have a look at ry1.
3. ADFE is a rectangle and GC//FA (// means is parallel to). What is the shape of quadrilateral CDEG ?

!
a) rectangle
b) trapezoid
c) right trapezoid
d) quadrilateral
A quadrilateral with exactly one pair of parallel sides is called a ... .
4. ADFE is a rectangle and GC//FA (// means is parallel to). What is the area of quadrilateral CDEG ?

!
a) 35 cm.2
b) 35/2 cm.2
c) 75/2 cm.2
d) 40 cm.2
Remember the previous questions .
5. ABCD is a rhombus; EF//DB. What is m(∠EFD) ?

!
a) 78°
b) 75°
c) 60°
d) 90°
Diagonals of a rhombus are perpendicular .
6. What is a parallelogram whose diagonals are equal ?

a) parallelogram
b) trapezoid
c) tetrahedral
d) rectangle
Draw parallelograms and see what happens as the lengths of diagonals get closer and closer .
7. What are the minimal and maximal possible lengths for AB as the ∠C varies ?

!


a) 4 cm. and 18 cm.
b) 0 cm. and 18 cm.
c) 4 cm. and infinite
d) 0 cm. and infinite
Remember triangle inequality .
8. All sides are equal and of unit length. How long is the perimeter of the figure shown below ?

!


a) 6 units
b) 12 units
c) 8 units
d) 14 units
Interior sides are not included as we consider perimeters .
9. All sides are of unit length. How big is the purple area ?

!


a) 1 unit square
b) 1/2 unit square
c) 2 unit square
d) 2/3 unit square


The whole square is of unit area .
10. ABC is a right triangle having legs of length 3 cm. and 4 cm. How long is the hypotenuse (try to decide counting on your vision)?

!


a) 6 cm.
b) 9/2 cm.
c) 5 cm.
d) 4 cm.
3-4- ... right triangle is a well known triangle. Pythegorean Thorem gives the length of its hypotenuse but it is too early to learn this theorem. We wanted you to get acquainted with the triangle and to find the length of the hypotenuse with the facts you already know.
11. Which choice is triangle inequality ?

a) In case of a triangle the sum of first two sides is greater and the difference of them is less than the 3rd side
b) In case of a triangle the sum of any two sides is greater and the difference of them is less than the remaining side.
c) In case of a triangle the sum of first two sides and the difference of them is less than the 3rd side
d) In case of a triangle the sum of first two sides and the difference of them is greater than the 3rd side
Just for remembrance because of importance .
12. Which shape can not be obtained by using equilateral triangles side by side ?

!


a) rhombus
b) parallelogram
c) trapezoid
d) square
Just two of them make a rhombus .
13. Which figure can be obtained without changing the length of matches ?

!
a) parallelogram
b) trapezoid
c) rectangle
d) square
i.e. only the angles can be changed .
14. If 6 matches are taken away and 2 squares left they will be ... .

!
a) adjacent
b) one inside of other
c) only two squares not attainable
d) adjacent or one inside other
Just count the number of matches and decide .
15. Assuming each unit with 4 matches around is a perfect square, which figure has a smaller area to perimeter ratio and what is this ratio if a match is accepted as the unit of length ?

!


a) II ; 1/2
b) II ; 1
c) I ; 1
d) I ; 1/2
Just count.
16. How big is the perimeter of the figure below ?

!


a) 50 cm.
b) 52 cm.
c) 54 cm.
d) 56 cm.
11 cm + 11 cm + 8 cm + 8 cm + 4 cm + 4 cm + 5 cm + 5 cm = .
17. How long does the car travel if the tire makes 1000 revolutions ?

!


a) 2 km.
b) 2170 m.
c) 2350 m.
d) 1250 m.
Take π = 3.1 .
18. |CB| = 20 cm. OD is the radius. What is the area of the half circle if π is taken as 3.14 ?

!


a) 117 cm.
b) 628 cm.
c) 328 cm.
d) 314 cm.2
Area is πxr2 = 3.14 x 100 .
19. It is asked to replace just 2 matches and to attain 4 squares. Which ones should be moved ?

!


a) 2 and 8
b) 4 and 8
c) 2 and 4
d) 4 and 10
2 and ... .
20. How much will the circumference of the World change if its radius is increased by 1 cm. ?

!


a) 6 cm.
b) 6 km.
c) 600 m.
d) 600 km.
Take π = 3 .
21. How many cm2 is the area of the triangle ABC ?

!


a) 20
b) 10
c) 35
d) 30
Just to understand that the area of a triangle is (base x height)/2 .
y
22. What are the base angles of the upper triangle ?

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

RY1 RY2



a) 35° and 41°
b) 39° and 21°
c) 45° and 46°
d) 39° and 41°


Have a look at the ry1 .
23. What is the sum of interior angles of the figure given below ?



a) 900°
b) 1200°
c) 1150°
d) 1080°
It has reflex angles but still a simple octagon .
24. How come is the sum of exterior angles of the figure given below is 360° ?



a) The exterior of a reflex angle (into the figure) is considered to be negative.
b) It is not.
c) The number of triangles are considered.
d) Reflex angles are reflexive
360° - the measure of the reflex angle = the measure of the turn up to that point and 360° being a perigon is considered to be 0°
Negative angle means that if the turn were "such and such" degrees more, a perigon would be completed.
25. How many reflex angles are there in the figure below ?



a) 2
b) 6
c) 3
d) 0
Simple last questions are almost trend.
This is the feedback!

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

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