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FOURTH GRADE / MATHEMATICS /BASICS of GEOMETRY 1.2

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

   BASICS of GEOMETRY ARE
 ♦ 
POINTS, LINE SEGMENTS, RAYS, LINES (INTERSSECTING or PARALLEL) and ANGLES.
 ♦ THEY ARE OUR BASIC BLOCKS ON THE WAY TO UNDERSTAND, ANALYZE and SYNTHESIZE SHAPES

THERE ARE TWO GOLDEN RULES:
1. THEY ARE IDEALIZATIONS FROM OUR DAILY EXPERIENCES.
2. BEING THOUGHT OBJECTS THEY MAY LEAD AMOK; SO BE CAREFUL WITH THEM.
y
1. That O is the midpoint of BD is indicated in the figure.
Find the value W if |BO| = 4xW - 7 and |OD| = 5xW - 35 .

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



a) 28
b) 32
c) 26
d) 34


"Equations" may be a terrifying noun but it should not be. See how simple they are in ry1.
y
2. In addition to the figure we have: |AO| = 5xW , |OC| = 6xW-22 and |AC| = 33
What should then W be equal to ?


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

RY1 RY2



a) 7
b) 9
c) 5
d) 11
As we do mathematics we mostly ignore physics and units. Look at the joke about our math. prof. and understand.
Do not "overmathematics", the danger is to create the whole Universe from a dimensionless point.
3. How many degrees is the angle with a "?" in it ?

!


a) 80
b) 65
c) 70
d) 75
Just read the protractor. It is something between 70 and 80 .
4. What is called the ray OB that divides the angle COA into two congruent angles of equal measure ?

!


a) sector
b) bisector
c) equal divider
d) cosector
The angles COB and BOA are congruent but not equal. Their measures are equal but not their direction .
5. How do we call the angles COB and BOA in the figure of question 4 ?

a) adjacent
b) adjoint
c) neighbor
d) adjoining
adjacent means lying near, close, or contiguous; adjoining .
6. Vertical angles (from vertex) are two angles whose sides form two pairs of opposite rays.
What is the figure below trying to prove about vertical angles ?

!


a) vertical angles are equal
b) vertical angles have equal measures, they are congruent
c) vertical angles are acute
d) vertical angles have a common vertex
In question 24 of our previous test we called "interior opposite angles" and now we refine our terminology .
The figure is proving the claim made there.
7. If a plane figure, how many right angles you can see ?

!


a) 0
b) 1
c) 2
d) 4
That the figure is on the plane is very important. There is at least 1.
8. The angles AOB and BOC are called ... . ?

!


a) conjugate
b) adjoint
c) complementary
d) supplementary
Complementary angles are 2 angles whose whose measures add up to 90 degrees .
9. What are the angles in the figure called ?

!


a) adjoining
b) neighbor
c) complementary
d) supplementary


Supplementary angles are 2 angles whose whose measures add up to 180 degrees .
10. What will be the in degrees measure of the angle with the question mark in it ?

!

a) 42
b) 40
c) 36
d) 38
Alltogether they make 90 degrees .
11. The measures of angles are written inside of each. What is W expected to be (in degrees) ?

!


a) 30
b) 25
c) 35
d) 27
All given says 6W = 180.
12. How big (in deg.) is the angle between the vane and the hour-arm ?

!


a) 30
b) 60
c) 45
d) 55
1 minute corresponds to 6 degrees.
13. Which of the statements in the following figure is/are true ?

!
a) I and III
b) I and II
c) II and III
d) all
Rays are directed .
14. What is the vertex of < (angle) 3 ?

!
a) B
b) C
c) O
d) A
< 3 and < 4 have a common vertex .
15. How are angles 5 and 6 ?

!


a) adjacent
b) adjoint
c) supplementary
d) complementary
We will give a proof soon, but know from today that the sum of inner angles of a triangle make 180 degrees . And of course angle 4 is 90 degrees which leaves 90 for the other two.
16. How many angles have C as the vertex ?

!


a) 2
b) 1
c) 3
d) none
Do consider the direct angle also .
17. How many angles are formed between W noncollinear (not forming the same line) rays that have the same endpoint ?

!


a) W-2
b) W+1
c) W
d) W-1
3 rays 2 angles ; 4 rays 3 angles ... .
18. Answer the question in the following figure .

!


a) 53
b) 41
c) 37 degrees
d) 39
Be careful about the unit and do use the given numbers, not your eye .
19. How many angles are formed between 15 noncollinear (not forming the same line) couples of opposite rays that are grouped into 3 groups such that all 3 have 5 couples of opposite rays emerging from a different endpoint ?

a) 14
b) 12
c) 9
d) 10
Remember endpoints may be translated. Even if not so, lines do intersect somewhere and form angles .
20. How many times the hands of a clock constitute a straight angle in a day ?

a) 2
b) 24
c) 22
d) 44
Till the hour-hand makes two turns the vane makes makes 24 full turns.
If the hour-hand stood still, there would be 24 direct angles.
21. Find the angle (in degrees) which exceeds thrice its complement by 10 degrees ?

a) 80
b) 70
c) 85
d) 65
A is the angle, C is the complement . We have A+C = 90 and 3xC + 10 = A
If we replace A we find 4xC + 10 = 90 and C = 20
y
22. What is the measure of < DOE with the given values of the figure below ?

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

RY1 RY2



a) m
b) m/2
c) (n+m)/2
d) n/2


Think by separating . A part is given in ry1 and another in ry2 .
Thus m(< EOB) = m + n/2 - m/2 = m/2 + n/2 .
This of course means : measure of < DOE = m/2
23. How many congruent group of angles do you see in the yellow colored region ?



a) 3
b) 4
c) 2
d) 5
The angle at the top (108 degrees) is divided into 3 angles (36 degrees) and each of them are congruent .
There are two other groups one group being 72 and the other being again 108 degrees.
24. How many angles of measure 72 degrees do you see in the yellow colored region of the figure of question 23 ?

a) 1
b) 2
c) 3
d) 4
The sum of two adjacent 36 deg. angles is a 72 deg. angle.
25. Which is the angle (in degrees) whose supplement is 3 thrice its complement ?

a) 60
b) 55
c) 35
d) 45
180 - W = 3x(90 - W) .
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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