Free Practical Geometry 02 Practice Test - 7th grade 

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.

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.

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 angles are equal i.e., $\angle$2 = $\angle$8 and $\angle$3 = $\angle$5.

(ii) Alternate exterior angles are equal i.e., $\angle$1 = $\angle$7 and $\angle$4 = $\angle$6.

(iii) Corresponding angles are equal i.e., $\angle$1 = $\angle$5, $\angle$4 = $\angle$8, $\angle$2 = $\angle$6 and $\angle$3 = $\angle$7.

(iv) Co-interior angles are supplementary i.e., $\angle$2 + $\angle$5 = 180${}^{\circ }$ and $\angle$3 + $\angle$8 =180${}^{\circ }$

$\angle$1 = $\angle$8 is incorrect.

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 $zcm$.

$z^2=3^2+4^2$

$z=\sqrt{25}$

$z=5\text{cm}$

When a line segment is perpendicular to another line segment then angle between them is ${90}^{\circ }$.

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.

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

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.

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