**Biconditional statements and definitions worksheet :**

Worksheet given in this section is much useful to the students who would like to practice problems on definitions and biconditional statements.

**Problem 1 :**

Whether each statement about the diagram is true. Explain your answer using the definitions you have learned.

(i) Points D, X and B are collinear.

(ii) AC is perpendicular to DB.

(iii) ∠AXB is adjacent to ∠CXD.

**Problem 2 :**

Write the following biconditional statement as a conditional statement and its converse.

**Biconditional Statement :**

"Three lines are coplanar if and only if they lie in the same plane"

**Problem 3 :**

Consider the following statement :

x = 3 if and only if x² = 9

(i) Is this a biconditional statement ?

(ii) Is the statement true ?

**Problem 4 :**

Each of the following statements is true. Write the converse of each statementand decide whether the converse is true or false. If the converse is true, combine it with the original statement to form a true biconditional statement. If the converse is false, state a counterexample.

(i) If two points lie in a plane, then the line containing them lies in the plane.

(ii) If a number ends in 0, then the number is divisible by 5.

**Problem 1 :**

Whether each statement about the diagram is true. Explain your answer using the definitions you have learned.

(i) Points D, X and B are collinear.

(ii) AC is perpendicular to DB.

(iii) ∠AXB is adjacent to ∠CXD.

**Solution : **

(i) This statement i s true. Two or more points are collinear, if they lie on the same line. The points D, X and B all lie on line DB. So thery are collinear.

(ii) This statement is true. The right angle symbol in the diagram indicates that the lines AC and BD intersect to form a right angle. So, the lines are perpendicular.

(iii) This statement is false. By definition, adjacent angles must share a common side. Because ∠AXB and ∠CXD do not share a common side, they are adjacent.

**Problem 2 :**

Write the following biconditional statement as a conditional statement and its converse.

**Biconditional Statement :**

"Three lines are coplanar if and only if they lie in the same plane"

**Solution : **

**Conditional Statement: **

If three lines are coplanar, then they lie in the same plane.

**Converse:**

If three lines lie in the same plane, then they are coplanar.

**Problem 3 :**

Consider the following statement :

x = 3 if and only if x² = 9

(i) Is this a biconditional statement ?

(ii) Is the statement true ?

**Solution : **

(i) The statement is biconditional because it contains “if and only if.”

(ii) The statement can be rewritten as the following statement and its converse.

**Conditional statement :**

If x = 3, then x² = 9.

**Converse :**

If x² = 9, then x = 3.

The first of these statements is true, but the second is false. Because, if x² = 9, then x = 3 or -3.

So, the biconditional statement is false.

**Problem 4 :**

Each of the following statements is true. Write the converse of each statementand decide whether the converse is true or false. If the converse is true, combine it with the original statement to form a true biconditional statement. If the converse is false, state a counterexample.

(i) If two points lie in a plane, then the line containing them lies in the plane.

(ii) If a number ends in 0, then the number is divisible by 5.

**Solution : **

**Solution (i) :**

**Converse :**

(i) If a line containing two points lies in a plane, then the points lie in the plane.

The converse is true, as shown in the diagram. So, it can be combined with the original statement to form the true biconditional statement written below.

**Biconditional statement : **

Two points lie in a plane, if and only if the line containing them lies in the plane.

**Solution (ii) : **

**Converse : **

If a number is divisible by 5, then the number ends in 0. The converse is false. As a counterexample, consider the number 15. It is divisible by 5, but it does not end in 0, as shown below.

20 ÷ 5 = 4

**25 ÷ 5 = 5**

30 ÷ 5 = 6

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

Apart from the stuff given above, if you want to know more about "Definitions and biconditional statements", please click here

Apart from the stuff given in this section, 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**