# LINES AND ANGLES WORKSHEET

## About "Lines and angles worksheet"

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.

## Lines and Angles Worksheet - Problems

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

## Lines and Angles Worksheet - Solution

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

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

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

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

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

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

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

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

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6