From a point P outside line segment AB = 6 cm, construct a line PQ parallel to line segment AB.
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Mathematics
Grade 7
Construction of a line paralle...
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From a point P outside line segment AB=6cm, construct a line PQ parallel to AB
AB
.
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Hint: To draw a parallel from a line segment to a point outside the line segment, firstly draw a line segment AB=6cm, then mark a point P outside of the line segment. Join the point P to the line segment. Measure the angle which the line from the point P makes with the line segment AB
AB
by making an arc and retrace the angle at the point P. Now, measure the length of the arc that intersects the line from the point P and the line segment AB
AB
and make a second arc on the retraced angle at the point P. Join the point P with the intersection of the arcs. We get a line parallel to the line segment AB
AB
.
Complete step-by-step solution:
Parallel lines are a set of lines which never intersect no matter how far the lines are stretched. These can be compared to the train tracks that always run parallel to each other but never intersect. These lines have certain properties which will help us in the construction of these parallel lines. We will see those properties as we proceed.
According to the question, we have to construct a parallel line from a line with a given length (line segment) to a point which is outside of that line segment. We will do step wise construction:
Step 1: Draw a line AB=6cm and label it as well.
Step 2: Now, mark a point P, anywhere outside the line segment AB
AB
Step 3: Join the point P to a point (let’s say C) on the line segment AB
AB
, we have
We know that parallel lines have congruent corresponding angles, we will use this property of the parallel lines to construct the parallel lines.
Step 4: Taking point C as the centre makes an arc intersecting the line PC
PC
and the line segment AB
AB
.
Step 5: Similarly, draw an arc taking P as the centre, we have,
Step 6: Now the length of the arc intersecting the line segment AB
AB
and the line PC
PC
, that measure the arc DE
DE
and make a second arc taking the point F as the centre, and then join the intersection of the arcs with the point P. We get
Therefore, we obtain PQ
PQ
parallel to the line segment AB
AB
.
To check whether the lines we obtained are parallel or not, we will use the property that in parallel lines the corresponding angles are equal. That is, we have to check if
∠DCB=∠FPQ∠DCB=∠FPQ
or not. Measuring these angles, we get the values of these angles as:
∠DCB=71.56∘∠DCB=71.56∘
∠FPQ=71.56∘∠FPQ=71.56∘
So, we see that both these angles are equal, therefore, we obtained parallel lines
Step-by-step explanation:
1) draw a line AB= 6cm
2) Take point P out side the line AB and take Point C on the line AB
3) Join P and C
4)using compass ,with convenient radius at C draw a arc to cut line AB and line PC
5) measure ED and Draw an arc to form F to cut the previous arc
6) draw a line from P and G to form parllel line AB
