Page 1 Points to Remember : Parallel Lines. Two lines in a plane which do not meet even when produced in definitely in either direction, are known as parallel lines. The perpendicular distance between two parallel lines is the same everywhere. Parallel Segments. Two segments are parallel, if the corresponding lines determined by them are parallel. Parallel Rays. Two rays are parallel, if the corresponding lines determined by them are parallel. EXERCISE 12 | | DG ; AD | | GH | | BC | | EF Q. 3. Identify the parallel lines segments in each of the figure given below : Sol. (i) In the given figure, DE | | BC Q. 1. In the adjoining figure of a table, given below, name pairs of parallel edges of the top. Sol. In the given figure, the pairs of parallel edges are : AB | | CD and BC | | AD Q. 2. Name the groups of all possible parallel edges of the box, whose figure is shown below. Sol. In the given figure, pairs of all possible parallel edges are : AB | | HE | | DC | | GF ; BE | | CF | | AH Page 2 Points to Remember : Parallel Lines. Two lines in a plane which do not meet even when produced in definitely in either direction, are known as parallel lines. The perpendicular distance between two parallel lines is the same everywhere. Parallel Segments. Two segments are parallel, if the corresponding lines determined by them are parallel. Parallel Rays. Two rays are parallel, if the corresponding lines determined by them are parallel. EXERCISE 12 | | DG ; AD | | GH | | BC | | EF Q. 3. Identify the parallel lines segments in each of the figure given below : Sol. (i) In the given figure, DE | | BC Q. 1. In the adjoining figure of a table, given below, name pairs of parallel edges of the top. Sol. In the given figure, the pairs of parallel edges are : AB | | CD and BC | | AD Q. 2. Name the groups of all possible parallel edges of the box, whose figure is shown below. Sol. In the given figure, pairs of all possible parallel edges are : AB | | HE | | DC | | GF ; BE | | CF | | AH (ii) In the given figure, AB | | DC ; AD | | BC (iii) In the given figure, AB | | DC ; AD | | BC (iv) In the given figure, LM | | RQ, MP | | RS, PQ | | SL. (v) In the given figure, AB | | CD, CD | | EF, AC | | BD, CE | | DF, AB | | EF. Q. 4. Find the distance between the parallel lines l and m, using a set square. Sol. (i) Place the rular so that one of its measuring edges lies along the line l. Hold it firmly with one hand. Now place a set square with one arm of the right angle coinciding with the edge of the rular. Read off the distance between l and m on the set square which is 1.7cm. (ii) Place the rular so that one of the measuring edges of the rular lies along the line l. Hold it firmly with one hand and place a set square with one arm of the right angle coinciding with the edge of the rular. Read off the distance between the lines l and m on the set square which is 1.2 cm. Q. 5. In figure, l | | m. If AB l, CD l and AB = 2.3 cm., find CD. Sol. It is given that l | | m. Also AB l i.e. AB is the perpendicular distance between two parallel lines l and m. Page 3 Points to Remember : Parallel Lines. Two lines in a plane which do not meet even when produced in definitely in either direction, are known as parallel lines. The perpendicular distance between two parallel lines is the same everywhere. Parallel Segments. Two segments are parallel, if the corresponding lines determined by them are parallel. Parallel Rays. Two rays are parallel, if the corresponding lines determined by them are parallel. EXERCISE 12 | | DG ; AD | | GH | | BC | | EF Q. 3. Identify the parallel lines segments in each of the figure given below : Sol. (i) In the given figure, DE | | BC Q. 1. In the adjoining figure of a table, given below, name pairs of parallel edges of the top. Sol. In the given figure, the pairs of parallel edges are : AB | | CD and BC | | AD Q. 2. Name the groups of all possible parallel edges of the box, whose figure is shown below. Sol. In the given figure, pairs of all possible parallel edges are : AB | | HE | | DC | | GF ; BE | | CF | | AH (ii) In the given figure, AB | | DC ; AD | | BC (iii) In the given figure, AB | | DC ; AD | | BC (iv) In the given figure, LM | | RQ, MP | | RS, PQ | | SL. (v) In the given figure, AB | | CD, CD | | EF, AC | | BD, CE | | DF, AB | | EF. Q. 4. Find the distance between the parallel lines l and m, using a set square. Sol. (i) Place the rular so that one of its measuring edges lies along the line l. Hold it firmly with one hand. Now place a set square with one arm of the right angle coinciding with the edge of the rular. Read off the distance between l and m on the set square which is 1.7cm. (ii) Place the rular so that one of the measuring edges of the rular lies along the line l. Hold it firmly with one hand and place a set square with one arm of the right angle coinciding with the edge of the rular. Read off the distance between the lines l and m on the set square which is 1.2 cm. Q. 5. In figure, l | | m. If AB l, CD l and AB = 2.3 cm., find CD. Sol. It is given that l | | m. Also AB l i.e. AB is the perpendicular distance between two parallel lines l and m. Again CD l i.e. CD is the perpendicular distance between two parallel lines l and m. But the perpendicular distance between two parallel lines is always same everywhere. CD = AB = 2.3 cm. Q. 6. In the Fig. do the segments AB and CD intersect ? Are they parallel ? Give reasons for your answer. Sol. In the given figure, we see that the line segments AB and CD do not intersect. But, the corresponding lines determined by them will clearly intersect. So, the segment AB and CD are not parallel. Q. 7. Using set square and a rular, test whether l | | m in each of the following cases. Sol. (i) Place the rular so that one of its measuring edges lies along of its measuring edges lies along the line l. Hold it firmly and place a set square with one arm of the right angle coinciding with the edge of the rular. Draw the line segment AB along the edge of the set square as shown in figure. Slide the set square along the rular and draw some more segments CD and EF. We observe that AB = CD = EF. l | | m. (ii) Place the rular so that one of its measuring edges lies along the line l. Hold it firmly and place a set square with one arm of the right angle conciding with the edge of the rular. Draw the line segment AB along the edge of the set square. Slide the set square along the rular and draw some more segments CD and EF as shown in the figure. We observe that AB CD EF Hence l is not parallel to m. Q. 8. Which of the following statements are true and which are false ? (i) Two lines are parallel if they do not meet, even when produced. (ii) Two parallel lines are everywhere same distance apart. (iii) If two segments do not intersect, they are parallel. (iv) If two rays do not intersect, they are parallel. Page 4 Points to Remember : Parallel Lines. Two lines in a plane which do not meet even when produced in definitely in either direction, are known as parallel lines. The perpendicular distance between two parallel lines is the same everywhere. Parallel Segments. Two segments are parallel, if the corresponding lines determined by them are parallel. Parallel Rays. Two rays are parallel, if the corresponding lines determined by them are parallel. EXERCISE 12 | | DG ; AD | | GH | | BC | | EF Q. 3. Identify the parallel lines segments in each of the figure given below : Sol. (i) In the given figure, DE | | BC Q. 1. In the adjoining figure of a table, given below, name pairs of parallel edges of the top. Sol. In the given figure, the pairs of parallel edges are : AB | | CD and BC | | AD Q. 2. Name the groups of all possible parallel edges of the box, whose figure is shown below. Sol. In the given figure, pairs of all possible parallel edges are : AB | | HE | | DC | | GF ; BE | | CF | | AH (ii) In the given figure, AB | | DC ; AD | | BC (iii) In the given figure, AB | | DC ; AD | | BC (iv) In the given figure, LM | | RQ, MP | | RS, PQ | | SL. (v) In the given figure, AB | | CD, CD | | EF, AC | | BD, CE | | DF, AB | | EF. Q. 4. Find the distance between the parallel lines l and m, using a set square. Sol. (i) Place the rular so that one of its measuring edges lies along the line l. Hold it firmly with one hand. Now place a set square with one arm of the right angle coinciding with the edge of the rular. Read off the distance between l and m on the set square which is 1.7cm. (ii) Place the rular so that one of the measuring edges of the rular lies along the line l. Hold it firmly with one hand and place a set square with one arm of the right angle coinciding with the edge of the rular. Read off the distance between the lines l and m on the set square which is 1.2 cm. Q. 5. In figure, l | | m. If AB l, CD l and AB = 2.3 cm., find CD. Sol. It is given that l | | m. Also AB l i.e. AB is the perpendicular distance between two parallel lines l and m. Again CD l i.e. CD is the perpendicular distance between two parallel lines l and m. But the perpendicular distance between two parallel lines is always same everywhere. CD = AB = 2.3 cm. Q. 6. In the Fig. do the segments AB and CD intersect ? Are they parallel ? Give reasons for your answer. Sol. In the given figure, we see that the line segments AB and CD do not intersect. But, the corresponding lines determined by them will clearly intersect. So, the segment AB and CD are not parallel. Q. 7. Using set square and a rular, test whether l | | m in each of the following cases. Sol. (i) Place the rular so that one of its measuring edges lies along of its measuring edges lies along the line l. Hold it firmly and place a set square with one arm of the right angle coinciding with the edge of the rular. Draw the line segment AB along the edge of the set square as shown in figure. Slide the set square along the rular and draw some more segments CD and EF. We observe that AB = CD = EF. l | | m. (ii) Place the rular so that one of its measuring edges lies along the line l. Hold it firmly and place a set square with one arm of the right angle conciding with the edge of the rular. Draw the line segment AB along the edge of the set square. Slide the set square along the rular and draw some more segments CD and EF as shown in the figure. We observe that AB CD EF Hence l is not parallel to m. Q. 8. Which of the following statements are true and which are false ? (i) Two lines are parallel if they do not meet, even when produced. (ii) Two parallel lines are everywhere same distance apart. (iii) If two segments do not intersect, they are parallel. (iv) If two rays do not intersect, they are parallel. Sol. (i) True (ii) True (iii) False (iv) False. You Must Know Transversal. A line which intersects two or more given lines in a plane at different points is called a transversal to the given lines. Angles made by a transversal to Two Lines : Let l and m be two lines and a transversal t intersecting them at the points L and M respectively. Mark the angles 1 to 8 as shown in the figure. (i) Interior Angles. The angles whose arms include line segment LM are called interior angles. So 3, 4, 5, 6 are interior angles. (ii) Exterior Angles. The angles whose arms do not include the line segment LM are called exterior angles. So, 1, 2, 7 and 8 are exterior angles. (iii) Corresponding Angles. The pairs ( 1 and 5), ( 2 and 6), ( 4 and 8) and ( 3 and 7) are the possible pairs of corresponding angles. (iv) Alternate Interior Angles. The pairs ( 3 and 5), and ( 4 and 6) are the possible pairs of alternate interior angles. (v) Alternate Exterior Angles. The pairs ( 2 and 8) and 1 and 7 are the pairs of alternate exterior angles. Some Results : (a) If a transversal cuts two parallel lines then : (i) Alternate angles are equal. (ii) Corresponding angles are equal. (iii) The sum of the interior angles on the same side of the transversal is equal to 180º. (b) If a transversal cuts two lines such that any one of the following conditions is satisfied : (i) Pairs of alternate angles are equal ; (ii) Pairs of corresponding angles are equal ; (iii) The sum of the interior angles on the same side of the transversal is 180º, then the two lines are parallel.Read More

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