Samacheer Kalvi Class 6 Maths Solutions Term 2 Chapter 4 Geometry Exercise 4.2

Question 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.
Answer:

The steps to draw a perpendicular line are:

Step 1: Start by drawing a straight line segment AB that is 7 cm long. Pick any spot on this line and call it point P.

Step 2: Take a set square. Place its corner (which has a right angle) exactly on point P. Make sure one side of the set square's right angle lies perfectly along the line AB.

Step 3: Draw a new line, PQ, along the other side of the set square's right angle, going through point P.

Step 4: This new line, PQ, will be exactly perpendicular to your first line, AB, at point P. This means the angles formed, \( \angle APQ \) and \( \angle BPQ \), are both 90 degrees.
In simple words: First, draw a 7 cm line AB and mark a point P on it. Then, use a set square to draw a line (PQ) that crosses AB at point P, making a perfect 90-degree angle.

🎯 Exam Tip: Always use a sharp pencil and a ruler for accurate measurements and a set square to ensure perfect right angles when constructing perpendicular lines.

Question 2. Draw a line segment LM = 6.5 cm and mark a point X not lying on it. Using a set square construct a line perpendicular to LM through X.
Answer:

The steps to construct a perpendicular line through an external point are:

Step 1: First, draw a line segment LM that is 6.5 cm long. Then, place a point X somewhere not on this line, perhaps above it.

Step 2: Use your set square. Place one of its arms (the straight edges) exactly along the line LM. Slide it until the other arm (the one that forms the right angle) gently touches point X.

Step 3: Now, draw a straight line from point X downwards, following the edge of the set square, until it meets the line LM. Call the meeting point Y.

Step 4: The line XY you just drew is now perpendicular to the line LM at point Y.
In simple words: Draw a 6.5 cm line LM and mark a point X not on it. Using a set square, draw a line from X that meets LM at a right angle.

🎯 Exam Tip: When constructing a line perpendicular through an external point, ensure the set square's right angle aligns perfectly with both the existing line and the external point.

Question 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.
Answer:

The lines are parallel because the distance between them is the same at any two points when measured with a set square. This consistent distance confirms they will never meet.
In simple words: When you measure the distance between the two lines at different spots using a set square, the measurement is always the same. This means the lines are parallel.

🎯 Exam Tip: Remember that parallel lines always maintain the same distance apart and will never intersect, a fundamental concept in geometry.

Question 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 segment.
Answer:

The steps to draw a parallel line through an external point are:

Step 1: Draw a line segment MN that is 7.8 cm long. Then, place a point B somewhere above this line.

Step 2: Take your set square and place it below point B. Align one of the edges that makes a right angle with line MN. Put a ruler (scale) along the other edge of the set square.

Step 3: Keep the ruler very steady. Slide the set square upwards along the ruler until the edge that was touching the ruler now touches point B. Draw a new line through point B using this edge. Call this new line AB.

Step 4: The line MN you drew first is now parallel to the line AB you just made.
In simple words: Draw a 7.8 cm line segment (MN). Mark a point B 5 cm above it. Then, using a set square and ruler, draw a new line (AB) through point B that runs exactly parallel to MN.

🎯 Exam Tip: The key to drawing parallel lines using a set square and ruler is to keep the ruler absolutely still while sliding the set square along it.

Question 5. Draw a line and mark a point R above it at a distance of 5.4 cm Through R draw a line parallel to the given line.
Answer:

The steps to draw a parallel line at a specific distance are:

Step 1: Begin by drawing a straight line, let's call it AB. Choose any point on this line and label it Q.

Step 2: Place your set square with its right-angle corner at point Q. Make sure one side of the set square lies perfectly along the line AB. Now, mark a point R directly above Q, such that the distance from Q to R is 5.4 cm.

Step 3: Position a ruler and the set square as shown in the picture (with the ruler along one edge of the set square that is on line AB).

Step 4: Hold the ruler firmly in place. Carefully slide the set square along the ruler until its other edge (the one perpendicular to the ruler) touches point R. Draw a new line through point R along this edge. Call this line RS.

Step 5: The line RS you just drew is now parallel to the original line AB.
In simple words: Draw a line AB. Pick a point Q on it. Measure 5.4 cm straight up from Q and mark point R. Then, use a ruler and set square to draw a new line (RS) through R that is parallel to AB.

🎯 Exam Tip: Accuracy in measuring the distance (5.4 cm) and carefully sliding the set square along the ruler are crucial for correct construction of parallel lines.