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SIXTH GRADE / GEOMETRY / TEST 6.1.1

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

SOME OF OUR QUESTIONS ARE REALLY HARD, FOR THOSE THAT ARE SKILLED IN MATH.
SKIP THEM IN CASE NOT FOR YOU.

IF YOU DESIRE SO, WE CAN DISCUSS HARD/INTERESTING QUESTIONS IN OUR FORUM.

 GEOMETRY
    ♦ 
We have had a pretty strong introduction to geometry. The questions, some questions, in our 4th-Grade geometry tests are proper for 6th and a couple of following grades
    ♦ Sciences don't make much use of geometry, we don't either. It should be an applied teaching, it could be more of it; It is not.
    ♦ According to Rousseau geometry owes much to greed and vanity. He says geometry developed because of difficulties in sharing of family land; we say it helped much to an equal share. So we want to teach this beauty.
Reference-1
Reference-2
1. The figure is of a cube, what will be the measure of ‹ACE ?

!


a) none
b) 45°
c) 40°
d) 30°
You need trig to calculate such angles; it has it's time .
2. Again a cube: What will be the measure of ‹ACH ?

!


a) 65°
b) 60°
c) 55°
d) 45°
The sides of the triangle are all surface diagonals of a cube, digonals of congruent/equal squares .
3. How many degrees is the measure of the angle between 2 rays ?

!


a) 55
b) 65
c) 60
d) 75
Find first the indicated 2 right angles .
Take care of the 2 isosceles triangles .
4. How many degrees will ‹AOB be ?

!


a) 105
b) 90
c) 100
d) 110
Wind β which is equal ...
5. How many degrees is the angle with a question mark ?

!


a) 70
b) 85
c) 105
d) 90
The angle between purple line segments should be 90° because ...
2 triangles should have a total of 360°.
Angles whose sides are perpendicular are equal.
y
6. Which algebraic expression gives the answer to the question mark (of the figure) ?

!


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



a) 180° + α - β
b) 180° + α + β
c) 180° - α - β
d) 180° - α + β


Have please a look at ry1 .
ClickN KIDS Beginning Reading & Spelling Programs Teacher Created Resources ClickN KIDS Beginning Reading & Spelling Programs
7. How many degrees is the angle with a question mark in ?

!


a) 80
b) 75
c) 86
d) 77
The line segments at top and bottom are parallel .
The sum of angles to the right (180°-70°) is supposed to be equal to the left [unkown angle + (180°-130°)] .
Bisector divides the unknown angle into 2 and the sum of inner angles of a triangle ...
8. What is the measure of the angle questioned ?

!


a) 100°
b) 110°
c) 90°
d) 95°
There are 2 possibilities (note that these are consistent with each othar):
1- The sum of the outer angles of the triangle is 360° so find the 3rd outer ...
2- The supplementaries of the given angles are 30° and 60° so use the sum of the inner angles of a triangle ...
9. How many degrees is the measure of ‹BAC ?

!


a) 85
b) 80
c) 76
d) 77
Isosceles triangles do have equal base angles ... .
10. Which algebraic expression is m(‹O) if the segments BO and CO are bisectors of their respective angles ?

!


a) m(‹O) = 90° - m(‹A)/4
b) m(‹O) = -90° + m(‹A)/2
c) m(‹O) = 90° - m(‹A)/2
d) m(‹O) = 90° + m(‹A)/2
There are 2 triangles and their respective three angles always add to 180° .
1- m(‹O) = 180° - [m(‹B)+m(‹C)]/2 .
2- m(‹A) = 180° - [m(‹B)+m(‹C)]
2 ==> m(‹A/2) = 90° - [m(‹B)+m(‹C)]/2
1&2 ==> m(‹O) = 180° - [90° - m(‹A/2)] ...
11. m(‹a) = ?

!


a) 50°
b) 60°
c) 55°
d) 45°
Divide the quadrilateral into 2 triangles and the sum of inner angles of each ...
150° - (180° - 2·a) = 2·a - 30°
2 · (2·a - 30°) + 90° - a = 180° .
y
12. How many degrees is the measure of the angle being questioned ?

!


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

RY1 RY2



a) 105
b) 85
c) 95
d) 80
Have please a look at ry1.
3·a + 60° = 180° .
13. The circumcircle of the right triangle of question-11 is drawn and another inscribed angle that subtends the same arc (the base) is constructed. How many degrees is this new angle ?

!


a) 45
b) 50
c) 40
d) 55
Inscribed angles subtending the same arc are equal. Remember that one of the base angles of the right triangle was 50° and it should have a vertex angle of ...
A second way of solving: The inscribed angle subtending the same common arc with a central angle is half of the central.
14. Which of the following choices is true regarding the tangent-chord angle marked by "I" ?

!


a) Tangent Chord Angle = Intercepted Arc .
b) Tangent Chord Angle = Intercepted Arc/4 .
c) Tangent Chord Angle = Intercepted Arc/2 .
d) Tangent Chord Angle = 2 · Intercepted Arc .


Just like the inscribed angle ... .
15. What will be the value of m(‹A)?

!


a) 60°
b) 50°
c) 65°
d) 55°
The inscribed angle is 120° , central angle/chord will be 240° .
The rest 120° of the chord is twice the sum of the both tangent-chord angles.
The sum of the inner angles of a quadrilateral is 360° .
16. What should the value of "a" be ?

!


a) 20°
b) 10°
c) 15°
d) 12 1/2 °
18·a = 180° .
17. What is m(‹a) ?

!


a) 60°
b) 52 1/2 °
c) 55°
d) 57 1/2 °
The green line segments have equal lengths, take please care .
y
18. The circles are tangent to each other and the values of the two angles are given. What is the measure of the angle having a "?" in ?

!


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


a) 75°
b) 80°
c) 60°
d) 85°
Have please a look at ry1. If the 3 angles of the quadrilateral at right is found, 4th will be obtained by subtracting their sum from 360° .
One of the angles of the quadrilateral is right angle .
Yellow triangle is an isosceles one, its base angle is (180° - 155°)/2 .
One of the angles of the quadrilateral is tangent-chord angle .
19. What is the measure of the angle being questioned ?

!


a) 80°
b) 75°
c) 60°
d) 70°
The sum of the 2 upper/vertex angles of the quadrilateral is 360° - 220° = 140° .
The angle that completes this to 2·180° = 360° is 220°, the sum of the 2 angles having bisectors .
This means the sum of the base angles of the yellow tringle is 110° .
20. Which of the choices is true regarding "o", the measure of the angle "O" ?

!


a) o=(a-b)/2
b) o=(a+b)/2
c) o=(a+b)
d) o=(a-b)
The sum of the base angles of the triangle is [360° - (a+b)]/2 .
21. What is the measure of the red filled angle of the figure ?

!


a) 80°
b) 78°
c) 66°
d) 72°
The vertical angles of (light) yellow triangles have to be (66°+50°)/2 = 58° .
y
22. What is the measure of the red filled angle of the figure ?

!


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

RY1 RY2



a) 55°
b) 65°
c) 60°
d) 62°


Have please a look at ry1 .
23. How many degrees is m(‹AOB) supposed to be ?

!


a) 60°
b) 65°
c) 55°
d) 57°
Connect points A and be to have a 7 sided polygon whose sum of inner angles is (7-2)·180°=900° .
The sum of the angles given is 775° .
24. What is the measure of the red filled angle if each color has equal share ?

!


a) 32 1/2 °
b) 25°
c) 22 1/2 °
d) 28°
Tangent (chord) angle is half of central .
25. What is the measure of the angle being questioned if the pentagon is regular ?

!


a) 36
b) 45
c) 72
d) 28
Inscribed angle is half of central .
This is the feedback!

THANK YOU FOR YOUR VISIT; HOPE WE COULD BE OF USE.
FOR MUTUAL BENEFIT YOU MAY USE OUR FORUM.
© 2012 , İsmail GERMAN. ALL RIGHTS RESERVED
PLEASE PREFER GIVING LINK IF THAT SUFFICES

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SOLUTION
VIA
EDUCATION
VIA
GEOMETRY!
THE EARTH
IS A SPHERE
WITH
r=6000 km.
PER CAPITA
AGRICULTURAL
LAND
2500 m.2











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4- Something may be lacking, something not mentioned here may be lacking since we seem to be behind Chief Seattle and on the way to realize his predictions in spite of all our education.

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