Olympiad Mathematics - Practical Geometry
Exam Duration: 45 Mins Total Questions : 30
Which among the following is used to construct a triangle?
- (a)
The lengths of the three sides
- (b)
The perimeter of the triangle
- (c)
The measures of three angles
- (d)
The names of three vertices
In the given figure, find the measure of ∠RQT,if PQ =QR and ∠QPR=60o
- (a)
60o
- (b)
140o
- (c)
120o
- (d)
100o
A triangular sign board is isosceles. If the unequal side is 7 cm and one of the equal sides is 6 cm, what is the measure of the third side?
- (a)
5 cm
- (b)
6 cm
- (c)
7 cm
- (d)
Either (A) or (C)
Which of the following statements is incorrect?
- (a)
The sum of angles in a triangle is 2 right angles.
- (b)
The exterior angle of a triangle is equal to the interior angle of the triangle
- (c)
The hypotenuse is the longest side of a right angled triangle.
- (d)
All the above
Identify the true statement
- (a)
A triangle with 3 equal sides is isosceles
- (b)
A triangle with a 110o angle is right angled.
- (c)
A triangle with 3 acute angles is acute angled.
- (d)
A triangle with 2 equal sides is equilateral.
David folds a sheet of paper. The dotted lines as shown in the figure are the creases formed, which are named as I,m and n.
Which of the following is true?
- (a)
l // m
- (b)
l // n
- (c)
n // m
- (d)
Either (B) or (C)
David folds a sheet of paper. The dotted lines as shown in the figure are the creases formed, which are named as I,m and n.
What do you call the line n with respect to the lines l and m?
- (a)
n is a line parallel to l and m.
- (b)
n is a line parallel to l only.
- (c)
n is a transversal
- (d)
n is a line parallel to m only.
Which of the following is used to draw a line parallel to a given line?
- (a)
A protractor
- (b)
A set square
- (c)
A ruler
- (d)
A ruler and compasses
The measurements of ΔDEF are EF= 8.4 cm, ∠E = 103o and ∠F = 85o. Which of the following is correct?
- (a)
Δ DEF can be constructed
- (b)
Δ DEF is an obtuse angled triangle
- (c)
Δ DEF cannot be constructed.
- (d)
Δ DEF is an acute angled triangle.
Which of the following can be used to construct a 30o angle
- (a)
Construct a 60o angle using compasses and bisect it
- (b)
Construct a perpendicular bisector of a line segment
- (c)
Construct the bisector of any angle
- (d)
Construct an angle congruent to any given angle.
Study the steps of construction given.
Step 1: Draw a ray OA.
Step 2: With O as centre and any convenient radius drawn an arc MN to cut \(\vec { OA } \) at M.
Step 3: With M as centre and the same radius draw an arc to cut MN at P.
Step 4: With P as centre and the same radius, draw an arc to cut MN at Q.
Step 5: Draw OQ and produce it to D. An angle AOD is constructed.
What is the measure of \(\angle AOD\)
- (a)
60o
- (b)
30o
- (c)
120o
- (d)
45o
Which of the following is NOT constructed using a ruler and a set square?
- (a)
A perpendicular to a line from a point not on it.
- (b)
A perpendicular bisector of a line segment.
- (c)
A perpendicular to a line at a point on the line.
- (d)
A line parallel to a given line through a given point
Given PQ = 4 cm, QR = 3.5 cm and RP = 4.5 cm, what type of a triangle can be constructed?
- (a)
An acute angled triangle
- (b)
An obtuse angled triangle
- (c)
An equilateral triangle
- (d)
A right angled triangle
ΔPQR is constructed such that PQ = 5 cm,PR= 5 cm and \(\angle RPQ\) = 50o Identify the type of triangle constructed.
- (a)
An isosceles triangle
- (b)
An acute angled triangle
- (c)
An obtuse angled triangle
- (d)
Both (A) and (B)
Identify the false statement.
- (a)
A triangle with three equal sides is called an equilateral triangle.
- (b)
A triangle with a right angle is called a right angled triangle
- (c)
A triangle with two equal sides is called a scalene triangle.
- (d)
A right angled triangle has two acute angles and a right angle.
How many perpendicular lines can be drawn to a line from a point not on it?
- (a)
1
- (b)
2
- (c)
0
- (d)
Infinite
In ΔXYZ,\(\overline { XY } >\overline { YZ } >\overline { ZX } \) Which of the following is the smallest angle?
- (a)
X
- (b)
Z
- (c)
Y
- (d)
X = V = Z
\(\angle PQR\) is constructed with all its angles measuring 60o each. Which of the following is correct?
- (a)
Δ PQR is an equilateral triangle
- (b)
Δ PQR is isosceles triangle
- (c)
Δ PQR is a scalene triangle.
- (d)
Δ PQR is a right angled triangle.
A triangle is constructed as shown in the figure.
Which of the following is not correct about ΔDEF?
- (a)
Δ DEF has all its sides equal.
- (b)
Δ DEF is an acute angled triangle
- (c)
Δ DEF is a scalene triangle
- (d)
Δ DEF is not an equilateral triangle .
An isosceles triangle is constructed as shown in the figure
Which of the given statements is incorrect?
- (a)
\(\overline { PR } \) is the hypotenuse of ΔPQR
- (b)
ΔPQR is an equilateral triangle
- (c)
ΔPQR is a right angled triangle.
- (d)
If right angled ΔPQR has its equal angles measuring 45o each.
Which vertex ΔABC is right angled if \(\overline { AB } \)=8 cm, \(\overline { AC } \)=6cm and \(\overline { BC } \)=10cm?
- (a)
\(\angle C\)
- (b)
\(\angle A\)
- (c)
\(\angle B\)
- (d)
A or C
Which of the following are the measures of a triangle that can be constructed using the S.S.S.criterion?
- (a)
\(\overline { XY } \)=6cm \(\angle X\)=40o \(\angle Y\)=70o
- (b)
\(\overline { DE} \)=8 cm, \(\overline { EF} \)=7cm, \(\overline { FD} \)=9cm
- (c)
\(\overline { PQ} \)=4 cm, \(\overline { QR} \)=6cm, \(\overline { Q} \)=80o
- (d)
\(\overline { AB} \)=5 cm, BC=6cm, \(\angle C\)=80o
A line p and a point X not on it are given.Which of the following is used to draw a line parallel to p through X?
- (a)
Equal corresponding angles
- (b)
Congruent triangles.
- (c)
Angle sum property of triangles.
- (d)
Pythagoras' theorem
Given AB = 3 cm. AC = 5 cm. and \(\angle B\) = 300 ΔABC cannot be uniquely constructed, with AC as base, why?
- (a)
Two sides and included angle are given.
- (b)
The other two angles are not given.
- (c)
The vertex B cannot be uniquely located.
- (d)
The vertex A coincides with the vertex C.
Identify the criterion of construction of the equilateral triangle LMN given LM = 6 cm.
- (a)
S.A.S.criterion
- (b)
R.H.S.criterion
- (c)
A.S.A criterion
- (d)
S.S.S criterion
A right triangle DEF is constructed with DE = 5 cm, \(\angle F\) = 900 and DF = 4 cm.Choose the correct statement from the following.
- (a)
OE is the hypotenuse of \(\triangle DEF\)
- (b)
\(\angle E+\angle D\)= 90o
- (c)
EF= 3 cm
- (d)
All the above
A triangle can be constructed by taking its sides as
- (a)
1.8 cm, 2.6 cm, 4.4 cm
- (b)
2 cm, 3 cm, 4 cm
- (c)
2.4 cm, 2.4 cm, 6.4 cm
- (d)
3.2 cm, 2.3 cm, 5.5 cm
A triangle can be constructed by taking two of its angles as
- (a)
110°,40°
- (b)
70°, 115°
- (c)
135°,45°
- (d)
90°,90°
Which of the following set of angles could be the lengths of the sides of a right-angled triangle?
- (a)
3 cm, 4 cm, 6 cm
- (b)
9 cm, 16 cm, 26 cm
- (c)
1,5 cm, 3.6 cm, 3.9 cm
- (d)
7 cm, 24 cm, 26 cm
Which of the following steps is INCORRECT, while constructing \(\Delta\)LMN, right angled at M, given that LN = 5 cm and MN = 3 cm?
Step 1. Draw MN of length 3 cm.
Step 2. At M, draw MX \(\bot \) MN. (L should be some where on this perpendicular).
Step 3. With N as centre, draw an arc of radius 5 cm. (L must be on this arc, since it is at a distance of 5 cm from N).
Step 4. L has to be on the perpendicular line MX as well as on the arc drawn with centre N. Therefore, L is the meeting point of these two and \(\Delta\)LMN is obtained.
- (a)
Only Step 4
- (b)
Both Step 2 and Step 3
- (c)
Only Step 2
- (d)
None of these