6th Maths Term 2 Geometry Exercise 4.2 Solutions & Constructions

6th Maths: Term 2 Unit 4: Geometry

Exercise 4.2 - Questions with Answers & Solutions

Exercise 4.2

1. Draw a line segment AB = 7 cm and mark a point P on it. Draw a line perpendicular to the given line segment at P.
Perpendicular line construction at a point on line
Step 1 :
Draw a line AB = 7 cm and take a point P on the line
Step 2 :
Place the set square on the line in such a way that the vertex which forms right angle coincides with P and one arm of the right angle coincides with the line AB.
Step 3 :
Draw a line PQ through P along the other arm of the right angle at the set square.
Step 4 :
The line PQ is perpendicular to the line AB at P.
That is PQ ⊥ AB.
∠APQ = ∠BPQ = 90°
2. Draw a line segment LM = 6.5 cm and take a point P not lying on it. Using a set square construct a line perpendicular to LM through P.
Perpendicular line from external point
Step 1 :
Draw a line LM = 6.5 cm. Take a point P above the line LM.
Step 2 :
Place one of the arms of the right angle of a set square along the line LM and the other arm of its right angle touches the point P.
Step 3 :
Draw a line through the point P meeting LM at Q.
Step 4 :
The line PQ is perpendicular to the line LM at Q.
That is PQ ⊥ LM.
3. Find the distance between the given lines using a set square at two different points on each of the pairs of lines and check whether they are parallel.
Checking parallel lines 1
Checking parallel lines 2
Yes. They are parallel.
4. Draw a line segment measuring 7.8 cm. Mark a point B above it at a distance of 5 cm. Through B draw a line parallel to the given line segment.
Parallel line construction
Step 1 :
Draw a line segment xy = 7.8 cm and mark a point A on the line.
Step 2 :
Place the set square in such away that the vertex of the right angle coincides with A and one of the edges of right angle lies along XY mark the point B such that AB = 5 cm.
Step 3 :
Place the set square under the line XY and fix the scale touching the set square.
Step 4 :
Hold the scale firmly and slide the set square along the edge of the scale until the other edge touches the point B. Draw a line BC through B.
Step 5 :
The line BC is parallel to XY. That is, BC || XY.
5. Draw a line and mark a point R below it at a distance of 5.4 cm Through R draw a line parallel to the given line.
Parallel line construction below a line
Step 1 :
Using a scale draw a line AB and mark a point C on the line.
Step 2 :
Place the set square upside down such that the vertex of the right angle coincides with C and one of the edges of right angle lies along AB. Mark a point R below AB such that CR = 5.4 cm
Step 3 :
Place the setsquare below AB and fix the scale touching the set square.
Step 4 :
Hold the scale firmly and slide the set square down until the other edge touches the point R. Draw a line RS through R.
Step 5 :
The line RS is parallel to AB. That is RS || AB.