Construction Of Parallel Lines
Class 8th Mathematics West Bengal Board Solution
Lets Work Out 22
Question 1.Let’s see how many line segments parallel to the line XY are possible to draw through the point Z which in not on XY.
Answer:
Consider a line XY and a point Z above it
Parallel lines are those lines which do not intersect
Only one line can be drawn parallel to given line XY from point Z every other line from Z will intersect XY at any point
Question 2.
Habib has drawn a line segment PQ on his exercise book and he has also considered a point R outside the line segment PQ. Let’s draw a line, parallel to the line segment PQ that passes through R by a scale and a compass.
Answer:
Habib’s construction is
Now we have to draw a line passing through R and parallel to PQ
Step1: Using scale draw a line passing through R intersecting PQ at A
Step2: Keep the needle of compass on point A and mark an arc intersecting RA and AQ at X and Y respectively
Step3: Keeping the distance in the compass same as that of in step2 keep the needle of compass on point R and mark an arc intersecting AR at Z
Step4: Take distance XY in compass keep the needle of compass on point Z and mark an arc intersecting arc drawn in step3 at point S
Step5: Using scale draw a line passing through R and S
Thus RS || PQ
Question 3.
Megha draws and angle ∠ABC = 60° by a scale and a compass. Let’s take two pints P and Q on the rays BA and BC respectively. Let’s draw a straight line through the point P parallel to the ray BC and also draw a straight line through the point Q parallel to the ray BA.
Let D be the intersecting Point. Let’s write the type of quadrilateral that PBQD is.
Answer:
Let us first construct what Megha had drawn
∠ABC = 60° only using scale and compass
Step1: Draw a ray BC. Take any distance in compass keep the needle of compass on point B mark an arc intersecting BC at X
Step2: Keeping the same distance in compass as that in step1 keep the needle on point X and mark an arc intersecting the arc drawn in step1 at Y. Draw ray AB passing though Y ∠ABC = 60° is ready
Now the quadrilateral part
Step3: Take any points P and Q on BA and BC respectively
Constructing a line parallel to BC passing through P
Step4: Take the same distance in compass as that of in step1. Keep the needle on point P and mark an arc intersecting PA at M
Step5: Take distance XY in compass keep the needle of compass on point M and draw an arc intersecting arc drawn in step4 at N. Draw line passing through PN
Constructing a line parallel to BA passing through Q
Step6: Take the same distance in compass as that of in step1. Keep the needle on point Q and mark an arc intersecting QC at R
Step7: Take distance XY in compass keep the needle of compass on point R and draw an arc intersecting arc drawn in step6 at S. Draw line passing through QS which intersects line PN at D
From figure we have constructed
PD || BQ and BP || QD opposite sides of quadrilateral PBQD are parallel hence PBQD is a parallelogram