Olympiad Mathematics - Practical Geometry
Exam Duration: 45 Mins Total Questions : 30
Into what type of parts is a figure divided by bisecting it?
- (a)
Unequal
- (b)
Equal
- (c)
Triangular
- (d)
Perpendicular
What do you call two lines intersecting at a point?
- (a)
Perpendicular lines
- (b)
Parallel lines
- (c)
Bisectors lines
- (d)
Intersecting lines
An angle of 15° is drawn using a pair of compasses and a ruler. How is it done?
- (a)
Bisecting 60° angle
- (b)
Bisecting 60° and 120° angles.
- (c)
Bisecting 60° and then bisecting it again
- (d)
Bisecting a 60° and 180° angles
Two lines are said to be perpendicular to each other when they meet at _____ angle.
- (a)
180°
- (b)
90°
- (c)
60°
- (d)
360°
Identify the one with no definite length.
- (a)
\(\overleftrightarrow { AB } \)
- (b)
\(\bar { PQ } \)
- (c)
-XYZ
- (d)
\(\bar { MN } \)
\(\overleftrightarrow { AB } \) has no definite length.
A few lines in a plane have a point in common. What type of lines can they be?
- (a)
Intersecting lines
- (b)
Parallel lines
- (c)
Concurrent lines
- (d)
Either (A) or (C)
If the lines are only two, then they are intersecting lines. If there are more than two lines, then they are concurrent lines.
\(\vec { QZ } \) is the bisector of ㄥPQR. Which of the following is true?
- (a)
ㄥPQZ=ㄥPQR
- (b)
ㄥPQZ=ㄥZQR
- (c)
ㄥPQZ=\(\frac { 1 }{ 2 } \)ㄥPQR
- (d)
Both (B) and (C)
\(\vec { OZ } \) bisects ㄥPQR (Given)
Thus ㄥPQZ=ㄥZQR=\(\frac { 1 }{ 2 } \)ㄥPQR
X and Y are two distinct points in a plane. How many lines can be drawn passing (A) Intersecting lines through both X and Y?
- (a)
0
- (b)
1
- (c)
Only 2
- (d)
Infinitely many
X is the midpoint of \(\bar { AB } \) . If \(\bar { AX } \) =9.3 cm what is the measure of \(\bar { AB } \) ?
- (a)
4.65 cm
- (b)
18.6 cm
- (c)
9.3 cm
- (d)
18 cm
ㄥPQR=ㄥXYZ. If \(\vec { QM } \) bisects ㄥPQR, \(\vec { YN } \) bisects ㄥXYZ, which of the following statements are true?
(i) ㄥPQM + ㄥNYZ = ㄥPQR
(ii) ㄥMQR + ㄥXYN = ㄥXYZ
(iii) ㄥPQM = 2ㄥPQR
(iv) ㄥXYZ = 2ㄥMQR
- (a)
(i) and (ii) only
- (b)
(i) and (iv) only
- (c)
(ii) and (iii) only
- (d)
(i), (ii) and (iv) only
Given ㄥPQR= ㄥXYZ, \(\vec { QM } \) bisects ㄥPQR
and \(\vec { YN } \) bisects ㄥXYZ respectively.
⇒ ㄥPQM = ㄥMQR = ㄥXYN = ㄥNYZ
⇒ ㄥPQM + ㄥNYZ = ㄥPQR is true.
ㄥMQR + ㄥXYN = ㄥXYZ is true.
ㄥPQM = 2 ㄥPQR is false as
ㄥPQM = \(\frac { 1 }{ 2 } \) ㄥPQR.
ㄥ XYZ = 2 ㄥMQR is true since
2 ㄥ MQR = ㄥPQR= ㄥXYZ.
Hence (i), (ii) and (iv) are true.
\(\vec { BA } \bot \overleftrightarrow { XY } \). Which of the following statements are incorrect?
(i) ㄥABX + ㄥABY = 1800
(ii) ㄥABX = 2 right angles
(iii) ㄥABY = 900
(iv) ㄥXBY = 900.
- (a)
(i) and (ii) only
- (b)
(ii) and (iv) only
- (c)
(ii) and (iii) only
- (d)
(i) and (iv) only
Since \(\vec { BA } \bot \overleftrightarrow { XY } \)
ㄥABX = 90° and ㄥABY = 90°
∴ ㄥABX + ㄥABY = 180° is true.
ㄥABX = 90° ⇒ ㄥABX = 2 right angles is false.
ㄥABY = 90° is true.
ㄥXBY= 90° is false since
ㄥXBY= ㄥXBA + ㄥABY = 1800.
P and Q are the end points of a line segment \(\bar { PQ } \) . If R is any point on \(\bar { PQ } \), which of the given statements may be true?
- (a)
PR = QR
- (b)
PR<QR
- (c)
PR>QR
- (d)
All the above
Given that R is any point on \(\bar { PQ } \), R may be Icoser to P or Q or exactly in between P and Q.
Hence PR = QR or PR < QR or PR > QR may be true.
p || q. Cand D are two points on p and M and N are two points on q, such that M and N are exactly opposite to C and D respectively. Identify the true statement.
- (a)
CDNM forms a rectangle
- (b)
\(\bar { CM } =\bar { DN } \).
- (c)
Both (A) and (B)
- (d)
Neither (A) nor (B)
From the figure and the given data, clearly, CDNM is a rectangle. Also \(\bar { CM } =\bar { DN } \) as the distance between two parallel lines is the same throughout.
Lines p and q have a point M in common. Identify the correct statement.
- (a)
ㄥ1=-3
- (b)
ㄥ2=-3
- (c)
ㄥ3=ㄥ4
- (d)
ㄥ1=ㄥ2
From the given figure and data, it is clear that p and q are intersecting lines. So, the vertically opposite angles are equal.
ㄥ1=ㄥ3
An angle of 75° is drawn using a pair of compass and ruler by bisecting angles_______.
- (a)
60°
- (b)
60° and 90°
- (c)
0° and 90°
- (d)
120° and 180°
Sumit constructed an angle of 90° and trisected it. Measure of two angles taken together will be_______.
- (a)
20°
- (b)
40°
- (c)
600
- (d)
None of these
A line segment has___ end points.
- (a)
No
- (b)
2
- (c)
1
- (d)
3
Number of perpendicular bisectors on a line segment is_______.
- (a)
Three
- (b)
Five
- (c)
One
- (d)
Infinite
Number of set squares in a geometry box is______.
- (a)
0
- (b)
1
- (c)
2
- (d)
3
Which of the following steps is INCORRECT while constructing an angle of 60°?
Step-1 : Draw a line EF and mark a point o on it.
Step-2 : Place the pointer of the compass at O and draw an arc of convenient radius which cuts the line EF at point P.
Step-3 : With the pointer at A (as centre), draw an arc that passes through O.
Step-4 : Let the two arcs intersect at Q. Join OQ. We get \(\angle\)QOP whose measure is 60°.
- (a)
Only Step-1
- (b)
Both Step-2 and Step-3
- (c)
Only Step-3
- (d)
Both Step-3 and Step-4
Step-3 is incorrect it should be written as : with the pointer at P(as centre) now draw an arc that passes through O.
Which one of the following is not a closed figure
- (a)
- (b)
- (c)
- (d)
A closed figure is that figure which begins and ends at the same point. Figure b, c and dare closed figure. Z is an open figure.
It is 12 0' clock. Look at the clock hands. What is the measure of the angle they have formed?
- (a)
900
- (b)
1800
- (c)
2700
- (d)
360o
Its 3600
The vertex of an angle lies
- (a)
in its interior
- (b)
in its exterior
- (c)
on the angle
- (d)
inside the angle
The vertex of an angle lies on the angle.
If Anisha turns 90° to her left what would she be facing
- (a)
Chairs and tables
- (b)
Book shelves
- (c)
Windows
- (d)
Coffee Machine
Windows
If Anisha makes an about turn to get a book from a shelf. How many degrees would she be turning by?
- (a)
180o
- (b)
90o
- (c)
360o
- (d)
none of these
180o
State which of the following statement is true?
- (a)
Point has a size because we can see it as a thick dot on paper
- (b)
Any plane through a vertical line is vertical
- (c)
Any plane through a horizontal line is horizontal
- (d)
Two lines in a plane always intersect in a point.
Any plane through a vertical line is vertical
Pinky runs around a square field of side 75 m, Bobby runs around a rectangular field with length 160 m and breadth 105 m. Who covers more distance? What is the difference in distance covered?
- (a)
Bobby, 230 m
- (b)
Pinky 300 m
- (c)
Bobby, 530 m
- (d)
Pinky 265 m
Distance covered by Pinky in one round
= Perimeter of the square field by side 75 m
= 4 x length of a side
= 4 x 75 m = 300m
Distance covered by Bobby in one round
Perimeter of the rectangular field
= 2 x (length + Breadth)
= 2 x (160 m + 105 m)
= 2 x 265 m
=530m
ஃ Difference in distance covered = 530 m - 300 m = 230m
Hence Bobby covers 230 m more.
The line FJ is __________ of the circle.
- (a)
Diameter
- (b)
Chord
- (c)
Radius
- (d)
None of above
Diameter of the circle
A rectangular plot is\(12\frac { 1 }{ 2 } m\quad long\quad and\quad 10\frac { 2 }{ 3 } \)wide. What is its area?
- (a)
133.33 m2
- (b)
146.2 m2
- (c)
130.30 m2
- (d)
146.33 m2
Area of Rectangular plot \(12\frac { 1 }{ 2 } m\quad long\quad and\quad 10\frac { 2 }{ 3 } \\ =\frac { 25 }{ 2 } \times \frac { 32 }{ 3 } =\frac { 800 }{ 6 } =133{ .33m }^{ 2 }\)
Study the figure given.
If angle P = 60°, RT || QP and angle TRS = 65°
Then angle PRQ is
- (a)
65o
- (b)
55o
- (c)
60o
- (d)
45o
RT || QP
PR is a transversal
Angle PRT = angle QPR = 60°
∠PRS = ∠PRT + angle ∠TRS = 60 + 65° = 125°
Angle PRQ = 180° - ∠PRS = 180° - 125° = 55°.