Question

to construct a line parallel to a given line and passing to a given point outside the line​

Answer 1

STEPS:

1. Using your straightedge, draw a transversal through point P. This is simply a straight line which passes through P and intersects with given line. Drawing the line slanted will make the construction easier than if you draw the line vertical. Be sure to draw the line well above P.

2. Using the construction COPY AN ANGLE, construct a copy of the angle formed by the transversal and the given line such that the copy will be located UP at point P. The vertex of the copied angle will be point P.

3. When you draw the line to complete the angle copy, you will be drawing a line parallel to the given line.

Proof of Construction: By using the COPY AN ANGLE construction, we created two angles of equal measure (which are also congruent). In relation to the parallel lines, these two angles are positioned in such a manner that they are called corresponding angles. A theorem regarding parallel lines tells us: If two lines are cut by a transversal and the corresponding angles are congruent, the lines are parallel. (Change the words "corresponding angles" to "alternate interior angles" and you have the proof for the Alternate Method.)

Answer 2

Given : a line

To Find :  draw a line parallel to a given line from a point outside it  

Solution:

Step 1 :  Draw a line  segment AB

Step 2 :  take a  point X on AB

Step 3 : Draw an acute angle at X  ∠YXB

Step 4 :  Take a point  Z on on XY

Step 5    Using suitable compass width and taking X as center draw an arc intersecting XY at M and XB at  N

Step 6 : Keeping compass width same and taking Z as center draw an arc such that it intersect ZY at  P  

Step 7 : take compass width = MN  and  taking P as as center intersect the arc drawn in previous step at  Q

Step 8 : Draw a line segment CD passing through Z & Q

CD || AB

Learn More:

Draw a line m. Draw a line n which is parallel to line m at a distance ...

brainly.in/question/4729612

3. Draw a line segment of length 6.3 cm. Draw another line parallel ...

brainly.in/question/13695013