# Free Practical Geometry 02 Practice Test - 7th grade

### Question 1

If the distance between any two lines is always constant then the lines:

are parallel to each other

may not be parallel to each other

may be parallel to each other

are perpendicular to each other

#### SOLUTION

Solution :B and C

If the distance between any two lines is always constant then the lines may or may not be parallel. If the lines lie in the same plane, then they are parallel and if they are not, they are not parallel.

### Question 2

Pavan tried to draw a line parallel to a given line, 'l'. Few steps are shown below. What will be the next step?

Step 1: Mark a point A, not on the line 'l'.

Step 2: Mark point B on line 'l'.

Step 3: Draw line segment joining points A and B.

Step 4: Draw an arc with B as the centre, such that it intersects line 'l' at D and AB at E.

Draw another arc with the same radius and A as the centre, such that it intersects AB at F

Draw another arc with B as the centre and distance DE as the radius

Draw another arc with some other radius and A as the centre

Draw another arc with B as the centre and distance AB as the radius

#### SOLUTION

Solution :A

Following are the steps to draw a line parallel to a given line:

Step 1: Mark a point A, not on the line 'l'.

Step 2: Mark point B on line 'l'.

Step 3: Draw line segment joining points A and B.

Step 4: Draw an arc with B as the centre, such that it intersects line 'l' at D and AB at E.

Step 5: Draw another arc with the same radius and A as the centre, such that it intersects AB at F.

Step 6: Draw another arc with F as the centre and distance DE as the radius.

Step 7: Mark the point of intersections of this arc and the previous arc as G.

Step 8: Draw line 'm' passing through points A and G.

Line 'm' is the required parallel line.

### Question 3

In the figure shown, the two lines are parallel to each other. Which of the following options is incorrect?

∠1 = ∠8

∠6 = ∠8

∠2 = ∠8

∠4 = ∠8

#### SOLUTION

Solution :A

When two lines intersect each other, four angles are formed. The pair of angles which lie on the opposite sides of the point of intersection are called

vertically opposite angle. If two parallel lines are cut by a transversal:

(i)

Alternate interior anglesare equal i.e., ∠2 = ∠8 and ∠3 = ∠5.(ii)

Alternate exterior anglesare equal i.e., ∠1 = ∠7 and ∠4 = ∠6.(iii)

Corresponding anglesare equal i.e., ∠1 = ∠5, ∠4 = ∠8, ∠2 = ∠6 and ∠3 = ∠7.(iv)

Co-interior anglesare supplementary i.e., ∠2 + ∠5 = 180∘ and ∠3 + ∠8 =180∘∠1 = ∠8 is incorrect.

### Question 4

Ram drew a line segment AB of length 3cm and another line segment CB of length 4cm which is perpendicular to line segment AB. What is the length of the third side of the triangle?

6cm

2cm

#### SOLUTION

Solution :A

The triangle will be a right angled triangle as CB is perpendicular to AB .So, the third side can be easily calculated by using Pythagoras theorem.

Let the length of the third side be zcm.

z2=32+42

z=√25

z=5 cm

### Question 5

If line segment AB is perpendicular to CD then ∠DCA = ? (in degrees)

#### SOLUTION

Solution :When a line segment is perpendicular to another line segment then angle between them is 90∘.

### Question 6

In the shown figure, line segment BD is angle bisector of ∠ABC. Line segment BE is angle bisector of ∠ABD. Then ∠ABC=

#### SOLUTION

Solution :As stated in question line segment BD is angle bisector so, ABD=DBC.

So, ∠ABC=4∠ABE

### Question 7

If the sides of a triangle are 3 cm, 4 cm, and 5 cm. Then, the triangle formed is a/an _____ triangle.

right-angled

obtuse-angled

acute-angled

equilateral

#### SOLUTION

Solution :A

Let us construct the required triangle as follows:

Step 1:

Draw the base line XY of the length 3 cm.Step 2:

Use your compass to make an arc with centre at point Y and the radius 4 cm.Step 3:

Use your compass to make a circle with centre at point X and the radius 5 cm.Step 4:

The point of intersection between the arcs is named as X.

The triangle is completed by joining all these three points.

Now, from above construction we see that the triangle formed is a right angle triangle.

### Question 8

Pavan followed the steps given below to construct a triangle

Right-angled triangle LMN, with hypotenuse LN=8cm and side MN=5cm.

Step 1: Draw line 'l'.

Step 2: Mark a point on 'l' and name it M.

Step 3: Draw a line segment MN=5cm on 'l' .

Step 4: Construct a right angle XMN at M.

Step 5: Draw an arc with N as the centre and radius equal to 8cm, such that it intersects MX.

Step 6: Mark the point of intersection as L.

Step 7: Join points L and N.

Are the steps followed by him correct?

If it is correct then enter "Yes” if no then enter "No”.

#### SOLUTION

Solution :Following the above steps, we can construct a right angled triangle with the given measurements. So, the given steps are correct.

### Question 9

The lines shown below never meet at any point. So, these lines are not parallel. Say true or false.

True

False

#### SOLUTION

Solution :B

Parallel lines never intersect. Parallel lines are lines in a plane which do not meet, that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel.

### Question 10

Raman had to draw an isosceles triangle with base angles as 65∘ each and base length of 5cm. Raman said the given data is insufficient. Is he correct?

True

False

#### SOLUTION

Solution :B

We are given two angles and one side. So, data is sufficient and the triangle can be drawn.