Practical Geometry Test

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Practical Geometry Test - 2

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Question 1
1 / -0

In triangle PQR, if PQ = 5 cm, ∠P = 35^o and ∠Q = 60^o. Which criterion can be used to construct this triangle?

A
ASA

B
SSS

C
SAS

D
RHS

Solution

Since one side and two angles of the triangle are given, thus ASA criterion can be used to construct this triangle.
Question 2
1 / -0

Which among the following is true for the given triangle?

A

B

C

D

Solution

The exterior angle of a triangle is the sum of interior opposite angles.
Question 3
1 / -0

The criterion used to construct a triangle when one included angle and two sides of the triangle are given, is

A
SAS

B
SSS

C
RHS

D
ASA

Solution

If one included angle and two sides of a triangle are given, then the triangle can be constructed by SAS (side angle side) property.
Question 4
1 / -0

A scalene triangle can be constructed by taking sides as

A
1.2 cm, 2.6 cm and 1.2 cm

B
2 cm, 6 cm and 5 cm

C
3.6 cm, 0.4 cm and 3.2 cm

D
3.3 cm, 1.5 cm and 1.8 cm

Solution

If the sum of any two sides is greater than the third side, then a scalene triangle can be constructed (because all the sides are unequal to each other).

2 + 5 > 6;

6 + 5 > 2;

6 + 2 > 5

So, option 2 is correct.
Question 5
1 / -0

An isosceles triangle can be constructed by taking angles as

A

B

C

D

Solution

Option 1 is the answer because in an isosceles triangle, two angles are equal, and the sum of all the angles is 55 + 55 + 70 = .
Question 6
1 / -0

Which of the following sets of lengths could be the sides of an equilateral triangle?

A
2.5 cm, 2.6 cm and 5.6 cm

B
5 cm, 6 cm and 8 cm

C
2 cm, 2 cm and 2 cm

D
1.3 cm, 3.4 cm and 1.6 cm

Solution

All sides of an equilateral triangle are equal.

So, option 3 is the correct answer.
Question 7
1 / -0

In which of the following cases can a right-angled triangle at B be drawn?

A
AB = 4 cm, BC = 3 cm, CA = 5 cm

B
AB = 5 cm,

C
AB = 6 cm, BC = 8 cm, CA = 12 cm

D

Solution

A right-angled triangle at B can be constructed if:

(1) ∠B = 90^o

(2) Pythagoras theorem is followed:

=>

=>

=> 9 + 16 = 25

=> 25 = 25

Thus, this triangle can be a right-angled triangle.
Question 8
1 / -0

Which of the following statements is INCORRECT?

A
It is possible to construct a unique triangle if two angles are given along with the included side.

B
It is possible to construct a triangle with sides as 2 cm, 3 cm and 4 cm.

C
An angle of 10.5^o can be constructed using a compass and a ruler.

D
All of these

Solution

It is not possible to construct an angle of 10.5^o using a compass and a ruler.
Question 9
1 / -0

Which of the following steps is INCORRECT in construction of , if it is given that CA = 10 cm, BC = 8 cm and ?

Step (1): Draw a line segment BC = 8 cm.
Step (2): Draw an arc to construct angle at B.
Step (3): Draw a line segment CA = 10 cm from C.
Step (4): Intersect the line segments BC and CA.

A
Step 1

B
Step 2

C
Step 3

D
Step 4

Solution

Step (1): Draw a line segment BC = 8 cm.
Step (2): Draw an arc to construct angle 90^o at B.
Step (3): Draw a line segment CA = 10 cm from C.
Step (4): Intersect the line segments BC and CA.
Here, step (4) is incorrect because from C, the line segment drawn will intersect the line segment from B at point A.
Question 10
1 / -0

Arrange the following steps in CORRECT order to construct a triangle whose three sides are 4 cm, 6 cm and 7 cm.

Step (1): Draw a line segment measuring one of the given side lengths of the triangle, say 6 cm, and mark its end points as A and B. Use a ruler to carry out this step.
Step (2): Place the tip of the compass on one of the end points of the side AB (let's choose to place it on A) and draw an arc on either side of the line segment AB.
Step (3): Set the width of your compass equal to another given length, say 7 cm. Retain this width for the next step.
Step (4): Set the width of your compass equal to length of the third side, which is 4 cm.
Step (5): Join C with each of the points A and B to complete the triangle.
Step (6): Place the tip of the compass on B and draw another arc which cuts the previously drawn arc at some point (say C).

A
1-3-2-4-6-5

B
2-1-5-6-4-3

C
3-2-1-6-5-4

D
4-5-6-1-2-3

Solution

The CORRECT order to construct a triangle whose three sides are 4 cm, 6 cm and 7 cm.

Step (1): Draw a line segment measuring one of the given side lengths of the triangle, say 6 cm, and mark its end points as A and B. Use a ruler to carry out this step.

Step (3): Set the width of your compass equal to another given length, say 7 cm. Retain this width for the next step.

Step (2): Place the tip of the compass on one of the end points of the side AB (let's choose to place it on A) and draw an arc on either side of the line segment AB.

Step (4): Set the width of your compass equal to length of the third side, which is 4 cm.

Step (6): Place the tip of the compass on B and draw another arc which cuts the previously drawn arc at some point (say C). 1-3-2-4-6-5 is the correct order of construction of a triangle whose all sides are given.

Step (5): Join C with each of the points A and B to complete the triangle.
1-3-2-4-6-5 is the correct order of construction of a triangle whose all sides are given.
Question 11
1 / -0

Write T for true and F for false:

(1) A triangle with two sides and included angle given is constructed by SAS property.
(2) The exterior angle of a triangle is the difference between interior opposite angles of the triangle.
(3) 70^o, 55^o, 55^o can be three angles of a triangle.

A
1 - T, 2 - F, 3 - T

B
1 - F, 2 - T, 3 - T

C
1 - F, 2 - F, 3 - F

D
1 - T, 2 - T, 3 - T

Solution

(1) A triangle with two sides and included angle given is constructed by SAS property.
(2) The exterior angle of a triangle is the sum of the interior opposite angles.
(3) 70^o, 55^o, 55^o = 180^o (Angle sum property)
Question 12
1 / -0

Which of the following steps is INCORRECT in construction of triangle ABC using a ruler and a compass with AB = 5 cm, AC = 4.5 cm, .

(1) Draw a line AB, 5 cm long.
(2) Use the compass to construct a 60^o angle at A.
(3) Use a ruler to find C, such as AC is 4.5 cm long.
(4) Join A with C.

Thus, we have the triangle ABC.

A
Step 1

B
Step 2

C
Step 3

D
Step 4

Solution

The following are the correct steps to construct the triangle:

(1) Draw a line AB, 5 cm long.
(2) Use the compass to construct a 60^o angle at A.
(3) Use a ruler to find C, such as AC is 4.5 cm long.
(4) Join B with C.

Thus, we have the required triangle ABC.
Question 13
1 / -0

Arrange the steps marked (1) to (7) in CORRECT order to construct a line parallel to a given line through a given point by drawing corresponding angles:

Step (1): Locate the given line and the given point. The point will not be on the given line, but above or below it.
Step (2): Draw a line through the given point and any point on the given line. This is the transverse line you will use to draw two corresponding angles, which will help you form the parallel line.
Step (3): Prepare the compass. Set the compass to a width that is less than half of the line segment you constructed.
Step (4): Draw the first angle. Place the tip of the compass on the point where the transverse line intersects the given line. Draw an arc that intersects the transverse line and the given line.
Step (5): Draw a line through the given point and the point created by the two intersecting arcs. This line is parallel to the given line through the given point.
Step (6): Using the same compass width, place the tip of the compass on the given point. Draw an arc that intersects the transverse line above the given point, extending to just below the given point.
Step (7): Set the width of the compass to the width of the first angle you created. Using the width of the first angle, set the tip of the compass at the point on the transverse line above the given point, and draw an arc that intersects the arc created before this.

A
1-2-3-4-6-7-5

B
2-6-5-3-1-4-7

C
3-2-1-4-5-6-7

D
4-6-1-2-3-5-7

Solution

Following order is the correct order :
Step (1): Locate the given line and the given point. The point will not be on the given line, but above or below it.

Step (2): Draw a line through the given point and any point on the given line. This is the transverse line you will use to draw two corresponding angles, which will help you form the parallel line.

Step (3): Prepare the compass. Set the compass to a width that is less than half of the line segment you constructed.

Step (4): Draw the first angle. Place the tip of the compass on the point where the transverse line intersects the given line. Draw an arc that intersects the transverse line and the given line.

Step (6): Using the same compass width, place the tip of the compass on the given point. Draw an arc that intersects the transverse line above the given point, extending to just below the given point.

Step (7): Set the width of the compass to the width of the first angle you created. Using the width of the first angle, set the tip of the compass at the point on the transverse line above the given point, and draw an arc that intersects the arc created before this.

Step (5): Draw a line through the given point and the point created by the two intersecting arcs. This line is parallel to the given line through the given point.

The correct order is 1-2-3-4-6-7-5.