**Lines and angles worksheet :**

Worksheet given in this section is much useful to the students who would like to practice problems on parallel lines, perpendicular lines and angles formed by transversals.

**Problem 1 : **

Think of each segment in the diagram as part of a line.

Which of the lines appear to fit the descriptions given below ?

(i) Parallel to AB and contains D

(ii) Perpendicular to AB and contains D

(iii) Skew to AB and contains D

(iv) Name the plane(s) that contain D and appear to be parallel to plane ABE.

**Problem 2 : **

Construct a line that passes through a given point P and is perpendicular to a given line l.

**Problem 3 : **

Think of each segment in the diagram as part of a line.

Which of the lines appear to fit the descriptions given below ?

(i) Parallel to QR and contains S

(ii) Perpendicular to QR and contains S

(iii) Skew to QR and contains S

(iv) Name the plane(s) that contain S and appear to be parallel to plane QRVU.

**Problem 4 : **

In the diagram given below, list all pairs of angles that fit the description.

(i) Corresponding angles

(ii) Alternate exterior angles

(iii) Alternate interior angles

(iv) Consecutive interior angles

**Problem 1 : **

Think of each segment in the diagram as part of a line.

Which of the lines appear to fit the descriptions given below ?

(i) Parallel to AB and contains D

(ii) Perpendicular to AB and contains D

(iii) Skew to AB and contains D

(iv) Name the plane(s) that contain D and appear to be parallel to plane ABE.

**Solution (i) :**

CD, GH and EF are all parallel to AB. But, only CD passes through D and is parallel to AB.

**Solution (ii) :**

BC, AD, AE and BF are all perpendicular to AB. But, only AD passes through D and is perpendicular to AB.

**Solution (iii) :**

DG, DH and DE all pass through D and are skew to AB.

**Solution (iv) :**

Only plane DCH contains D and is parallel to plane ABE.

**Problem 2 : **

Construct a line that passes through a given point P and is perpendicular to a given line l.

**Solution : **

**Step 1 : **

Place the compass point at P and draw an arc that intersects line l twice. Label the intersections as A and B.

The diagram given below illustrates step 1.

**Step 2 : **

Draw an arc with center A. Using the same radius, draw an arc with center B. Label the intersection of the arcs as Q.

The diagram given below illustrates step 2.

**Step 3 : **

Use a straightedge to draw PQ. Now, PQ ⊥ l

**Problem 3 : **

Think of each segment in the diagram as part of a line.

Which of the lines appear to fit the descriptions given below ?

(i) Parallel to QR and contains S

(ii) Perpendicular to QR and contains S

(iii) Skew to QR and contains S

(iv) Name the plane(s) that contain S and appear to be parallel to plane QRVU.

**Solution (i) :**

UV, WX, and ST are all parallel to QR. But, only ST passes through S and is parallel to AB.

**Solution (ii) :**

QT, RS, RV and QU are all perpendicular to QR. But, only RS passes through S and is perpendicular to QR.

**Solution (iii) :**

ST and SW pass through S and are skew to QR.

**Solution (iv) :**

Only plane TSWX contains S and is parallel to plane QRVU.

**Problem 4 : **

In the diagram given below, list all pairs of angles that fit the description.

(i) Corresponding angles

(ii) Alternate exterior angles

(iii) Alternate interior angles

(iv) Consecutive interior angles

**Solution : **

**(i) Corresponding angles : **

∠ 1 and ∠ 5

∠ 2 and ∠ 6

∠ 3 and ∠ 7

∠ 4 and ∠ 8

**(ii) Alternate exterior angles : **

∠ 1 and ∠ 8

∠ 2 and ∠ 7

**(iii) ****Alternate interior angles : **

∠ 3 and ∠ 6

∠ 4 and ∠ 5

**(iv) Consecutive interior angles : **

∠ 3 and ∠ 5

∠ 4 and ∠ 6

After having gone through the stuff given above, we hope that the students would have understood "Lines and angles worksheet".

Apart from the stuff given above, if you want to know more about "Lines and angles", please click here

Apart from the stuff given on "Lines and angles worksheet", if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**