9th Class Math Notes Chapter-12

Mathematics Notes for 9th Class Exercise 12.1

by
Sharing is Caring
        
[post-views]

Mathematics Notes for 9th Class Exercise 12.1

“Math” a compulsory subject for 9th class Science students. and Mathematics Notes for 9th Class Exercise 12.1 or Math Notes Class 9 English Medium (Science Group) included in this book.

(DOWNLOAD IN PDF FORMAT)

Note: If you find any error, then just inform us in comments or email address admin@eStudent.pk

0%
1 votes, 1 avg
56

Revise / Test Your MCQs

Time is over

Thanks for taking Quiz, Click Finish Button to see your Result

Math Ch#12, 9th Class

Here MCQs for your Revision

For Good Revision & Grip on Concept, You Should take the MCQs and Revise it again and again

Good Luck. . . .  (:

Welcome

You Should Enter your Name

1 / 18

In any triangle, bisectors of _____ are concurrent (Similar)

2 / 18

Bisection of an angle means to draw a ray to divide the given angle into ____ equal parts.

3 / 18

Right bisector of any _________ means to draw perpendicular which passes through the midpoint of a line segment.

4 / 18

If the bisector of any angle of a triangle bisects side opposite to it, then the triangle is _______

5 / 18

If diagonals of a quadrilateral divide the figure in four congruent triable then the quadrilateral is  ____

6 / 18

How many mid points a line segment has?

7 / 18

The distance between a line and a point on same line is _________

8 / 18

A line segment has _____ midpoint

9 / 18

Any point inside an ____ equidistant from its arms is on the bisector of it.

10 / 18

Tight bisectors of sides of an obtuse angles triangle meet _______

11 / 18

Bisection means to divided the parallelogram into _______ triangles.

12 / 18

Right bisection of three sides of triangle are _______

13 / 18

The right bisector of the sides of a ___________triangle, intersect each other on the hypotenuse.

14 / 18

In any triangle, ______ of angles are concurrent.

15 / 18

The circumcenter is used to _____ about a triangle.

16 / 18

Angle bisector of triangle are _______Concurrent

17 / 18

Sum of interior angles of a quadrilateral is ________

18 / 18

In an acute angled triangle, _______ angles are less than 90 degree.

Your score is

Share  your Result with friends:

LinkedIn Facebook

You Can Follow eStudent.pk on

0%

Can u write your Feelings

How You Feel this

If you find any mistake in MCQs, please inform us by Commenting or by Contact us menu to improve the Quality of this free content.

Let’s see, How Students Solve this . . . . . . . Results  . . .

Click here to see the resultsSee Result

Math Solution 9th Class (Science Group)

Exercise 1.1           (English)            (Urdu)

Exercise 1.2           (English)            (Urdu)

Exercise 1.3           (English)            (Urdu)

Exercise 1.4           (English)            (Urdu)

Exercise 1.5           (English)            (Urdu)

Exercise 1.6           (English)            (Urdu)

Exercise 1-Rev      (English)            (Urdu)

Online Practice/ Test - MCQs & Short Questions

Exercise 2.1           (English)            (Urdu)

Exercise 2.2           (English)            (Urdu)

Exercise 2.3           (English)            (Urdu)

Exercise 2.4           (English)            (Urdu)

Exercise 2.5           (English)            (Urdu)

Exercise 2.6           (English)            (Urdu)

Exercise 2-Rev      (English)            (Urdu)

Online Practice/ Test - MCQs & Short Questions

Exercise 3.1           (English)            (Urdu)

Exercise 3.2           (English)            (Urdu)

Exercise 3.3           (English)            (Urdu)

Exercise 3.4           (English)            (Urdu)

Exercise 3-Rev      (English)            (Urdu)

Online Practice/ Test - MCQs & Short Questions

Exercise 4.1           (English)            (Urdu)

Exercise 4.2           (English)            (Urdu)

Exercise 4.3           (English)            (Urdu)

Exercise 4.4           (English)            (Urdu)

Exercise 4-Rev      (English)            (Urdu)

Online Practice/ Test - MCQs & Short Questions

Exercise 5.1           (English)            (Urdu)

Exercise 5.2           (English)            (Urdu)

Exercise 5.3           (English)            (Urdu)

Exercise 5.4           (English)            (Urdu)

Exercise 5-Rev      (English)            (Urdu)

Online Practice/ Test - MCQs & Short Questions

Exercise 6.1           (English)            (Urdu)

Exercise 6.2           (English)            (Urdu)

Exercise 6.3           (English)            (Urdu)

Exercise 6-Rev      (English)            (Urdu)

Online Practice/ Test - MCQs & Short Questions

Exercise 7.1           (English)            (Urdu)

Exercise 7.2           (English)            (Urdu)

Exercise 7.3           (English)            (Urdu)

Exercise 7-Rev      (English)            (Urdu)

Online Practice/ Test - MCQs & Short Questions

Exercise 8.1           (English)            (Urdu)

Exercise 8.2           (English)            (Urdu)

Exercise 8.3           (English)            (Urdu)

Exercise 8-Rev      (English)            (Urdu)

Online Practice/ Test - MCQs & Short Questions

Exercise 9.1           (English)            (Urdu)

Exercise 9.2           (English)            (Urdu)

Exercise 9.3           (English)            (Urdu)

Exercise 9-Rev      (English)            (Urdu)

Online Practice/ Test - MCQs & Short Questions

Exercise 10.1           (English)            (Urdu)

Exercise 10.2           (English)            (Urdu)

Exercise 10.3           (English)            (Urdu)

Exercise 10.4           (English)            (Urdu)

Exercise 10-Rev      (English)            (Urdu)

Online Practice/ Test - MCQs & Short Questions

Exercise 11.1           (English)            (Urdu)

Exercise 11.2           (English)            (Urdu)

Exercise 11.3           (English)            (Urdu)

Exercise 11.4           (English)            (Urdu)

Exercise 11.5           (English)            (Urdu)

Exercise 11-Rev      (English)            (Urdu)

Online Practice/ Test - MCQs & Short Questions

Exercise 12.1           (English)            (Urdu)

Exercise 12.2           (English)            (Urdu)

Exercise 12.3           (English)            (Urdu)

Exercise 12-Rev      (English)            (Urdu)

Online Practice/ Test - MCQs & Short Questions

Exercise 13.1           (English)            (Urdu)

Exercise 13.2           (English)            (Urdu)

Exercise 13-Rev      (English)            (Urdu)

Online Practice/ Test - MCQs & Short Questions

Exercise 14.1           (English)            (Urdu)

Exercise 14.2           (English)            (Urdu)

Exercise 14-Rev      (English)            (Urdu)

Online Practice/ Test - MCQs & Short Questions

Exercise 15           (English)            (Urdu)

Exercise 15-Rev   (English)            (Urdu)

Online Practice/ Test - MCQs & Short Questions

Exercise 16.1           (English)            (Urdu)

Exercise 16.2           (English)            (Urdu)

Exercise 16-Rev      (English)            (Urdu)

Online Practice/ Test - MCQs & Short Questions

Exercise 17.1           (English)            (Urdu)

Exercise 17.2           (English)            (Urdu)

Exercise 17.3           (English)            (Urdu)

Exercise 17.4           (English)            (Urdu)

Exercise 17.5           (English)            (Urdu)

Exercise 17-Rev      (English)            (Urdu)

Online Practice/ Test - MCQs & Short Questions

9th Math Science Group (English Medium)

9th Math Science Group (Urdu Medium)

9th Math Arts Group (Urdu Medium)

Mathematics Notes for 9th Chapter # 12:

Math Notes Class 9:

9th class math notes chapter 12, 9th class math solution chapter 12 pdf, math notes class 9 chapter 12, Math Notes Class 9 Exercise 12.1, exercise 12.1 class 9, Mathematics Notes for 9th Class Exercise 12.1 then this post is specially for you and your future. 

9th Class Math MCQs Chapter-12

by
9th Class Math MCQs Chapter-12

LINE BISECTORS AND ANGLE BISECTORS:

If you are searching the topic “9th Class Math Solution” & “9th Class Math MCQs Chapter-12” for matric classes then, you are on the right place, because we are providing the Quality material for education of Students and their problems.

Class 9 Math MCQs Chapter-12:

MCQs from Text Book Exercise and others included in this Practice panel. By practicing again and again, Student can get good practice on this topic “Line Bisectors and Angle Bisectors” i.e. 9th Class Math MCQs Chapter-12.

Best of Luck.

0%
1 votes, 1 avg
56

Revise / Test Your MCQs

Time is over

Thanks for taking Quiz, Click Finish Button to see your Result

Math Ch#12, 9th Class

Here MCQs for your Revision

For Good Revision & Grip on Concept, You Should take the MCQs and Revise it again and again

Good Luck. . . .  (:

Welcome

You Should Enter your Name

1 / 18

Bisection of an angle means to draw a ray to divide the given angle into ____ equal parts.

2 / 18

Tight bisectors of sides of an obtuse angles triangle meet _______

3 / 18

Bisection means to divided the parallelogram into _______ triangles.

4 / 18

The distance between a line and a point on same line is _________

5 / 18

Angle bisector of triangle are _______Concurrent

6 / 18

The right bisector of the sides of a ___________triangle, intersect each other on the hypotenuse.

7 / 18

If the bisector of any angle of a triangle bisects side opposite to it, then the triangle is _______

8 / 18

Right bisector of any _________ means to draw perpendicular which passes through the midpoint of a line segment.

9 / 18

Any point inside an ____ equidistant from its arms is on the bisector of it.

10 / 18

How many mid points a line segment has?

11 / 18

In an acute angled triangle, _______ angles are less than 90 degree.

12 / 18

Sum of interior angles of a quadrilateral is ________

13 / 18

A line segment has _____ midpoint

14 / 18

The circumcenter is used to _____ about a triangle.

15 / 18

In any triangle, bisectors of _____ are concurrent (Similar)

16 / 18

Right bisection of three sides of triangle are _______

17 / 18

In any triangle, ______ of angles are concurrent.

18 / 18

If diagonals of a quadrilateral divide the figure in four congruent triable then the quadrilateral is  ____

Your score is

Share  your Result with friends:

LinkedIn Facebook

You Can Follow eStudent.pk on

0%

Can u write your Feelings

How You Feel this

 

If you find any mistake in MCQs, please inform us by Commenting or by Contact us menu to improve the Quality of this free content.

Let’s see, How Students Solve this . . . . . . . Results  . . .

Click here to see the resultsSee Result

Math Solution 9th Class (Science Group)

Exercise 1.1           (English)            (Urdu)

Exercise 1.2           (English)            (Urdu)

Exercise 1.3           (English)            (Urdu)

Exercise 1.4           (English)            (Urdu)

Exercise 1.5           (English)            (Urdu)

Exercise 1.6           (English)            (Urdu)

Exercise 1-Rev      (English)            (Urdu)

Online Practice/ Test - MCQs & Short Questions

Exercise 2.1           (English)            (Urdu)

Exercise 2.2           (English)            (Urdu)

Exercise 2.3           (English)            (Urdu)

Exercise 2.4           (English)            (Urdu)

Exercise 2.5           (English)            (Urdu)

Exercise 2.6           (English)            (Urdu)

Exercise 2-Rev      (English)            (Urdu)

Online Practice/ Test - MCQs & Short Questions

Exercise 3.1           (English)            (Urdu)

Exercise 3.2           (English)            (Urdu)

Exercise 3.3           (English)            (Urdu)

Exercise 3.4           (English)            (Urdu)

Exercise 3-Rev      (English)            (Urdu)

Online Practice/ Test - MCQs & Short Questions

Exercise 4.1           (English)            (Urdu)

Exercise 4.2           (English)            (Urdu)

Exercise 4.3           (English)            (Urdu)

Exercise 4.4           (English)            (Urdu)

Exercise 4-Rev      (English)            (Urdu)

Online Practice/ Test - MCQs & Short Questions

Exercise 5.1           (English)            (Urdu)

Exercise 5.2           (English)            (Urdu)

Exercise 5.3           (English)            (Urdu)

Exercise 5.4           (English)            (Urdu)

Exercise 5-Rev      (English)            (Urdu)

Online Practice/ Test - MCQs & Short Questions

Exercise 6.1           (English)            (Urdu)

Exercise 6.2           (English)            (Urdu)

Exercise 6.3           (English)            (Urdu)

Exercise 6-Rev      (English)            (Urdu)

Online Practice/ Test - MCQs & Short Questions

Exercise 7.1           (English)            (Urdu)

Exercise 7.2           (English)            (Urdu)

Exercise 7.3           (English)            (Urdu)

Exercise 7-Rev      (English)            (Urdu)

Online Practice/ Test - MCQs & Short Questions

Exercise 8.1           (English)            (Urdu)

Exercise 8.2           (English)            (Urdu)

Exercise 8.3           (English)            (Urdu)

Exercise 8-Rev      (English)            (Urdu)

Online Practice/ Test - MCQs & Short Questions

Exercise 9.1           (English)            (Urdu)

Exercise 9.2           (English)            (Urdu)

Exercise 9.3           (English)            (Urdu)

Exercise 9-Rev      (English)            (Urdu)

Online Practice/ Test - MCQs & Short Questions

Exercise 10.1           (English)            (Urdu)

Exercise 10.2           (English)            (Urdu)

Exercise 10.3           (English)            (Urdu)

Exercise 10.4           (English)            (Urdu)

Exercise 10-Rev      (English)            (Urdu)

Online Practice/ Test - MCQs & Short Questions

Exercise 11.1           (English)            (Urdu)

Exercise 11.2           (English)            (Urdu)

Exercise 11.3           (English)            (Urdu)

Exercise 11.4           (English)            (Urdu)

Exercise 11.5           (English)            (Urdu)

Exercise 11-Rev      (English)            (Urdu)

Online Practice/ Test - MCQs & Short Questions

Exercise 12.1           (English)            (Urdu)

Exercise 12.2           (English)            (Urdu)

Exercise 12.3           (English)            (Urdu)

Exercise 12-Rev      (English)            (Urdu)

Online Practice/ Test - MCQs & Short Questions

Exercise 13.1           (English)            (Urdu)

Exercise 13.2           (English)            (Urdu)

Exercise 13-Rev      (English)            (Urdu)

Online Practice/ Test - MCQs & Short Questions

Exercise 14.1           (English)            (Urdu)

Exercise 14.2           (English)            (Urdu)

Exercise 14-Rev      (English)            (Urdu)

Online Practice/ Test - MCQs & Short Questions

Exercise 15           (English)            (Urdu)

Exercise 15-Rev   (English)            (Urdu)

Online Practice/ Test - MCQs & Short Questions

Exercise 16.1           (English)            (Urdu)

Exercise 16.2           (English)            (Urdu)

Exercise 16-Rev      (English)            (Urdu)

Online Practice/ Test - MCQs & Short Questions

Exercise 17.1           (English)            (Urdu)

Exercise 17.2           (English)            (Urdu)

Exercise 17.3           (English)            (Urdu)

Exercise 17.4           (English)            (Urdu)

Exercise 17.5           (English)            (Urdu)

Exercise 17-Rev      (English)            (Urdu)

Online Practice/ Test - MCQs & Short Questions

9th Math Science Group (English Medium)

9th Math Science Group (Urdu Medium)

9th Math Arts Group (Urdu Medium)

9th Class Math Solution:

We know, the importance of mathematics study in every class is important for students, such like students of 9th Class & 10th Class or other classes. If we talk Matric Classes Student of Science Classes or Arts classes, Math is equally important for both Classes.

Every Student of 9th & 10th Class is trying to search the topic like “9th Class math solution pdf”, 10th Class Math Solution PDF”, 9th Class Math MCQs Chapter-12, 9th Class Math Notes Chapter-12, Class 9 Math MCQs Chapter-12.

 

Class 9 Mathematics  Chapter-Wise MCQs

Category: 09th Math Startup

0%
4 votes, 4.8 avg
126

Revise / Test Your MCQs

Time is over

Thanks for taking Quiz, Click Finish Button to see your Result

Math Ch#4, 09th Class

Here MCQs for your Revision

For Good Revision & Grip on Concept, You Should take the MCQs and Revise it again and again

Good Luck. . . .  (:

Welcome

You Should Enter your Name

1 / 15

The degree of polynomial 4x^{4}+ 2x^{2}y  is ___________

2 / 15

x^{3}+\frac{1}{x^{3}} = \left ( x+\frac{1}{x} \right ) (_____________)

  • x^{2}-1+\frac{1}{x^{2}}
  • x^{2}+1+\frac{1}{x^{2}}
  • x^{2}-1-\frac{1}{x^{2}}
  • x^{2}+1-\frac{1}{x^{2}}

(Select Correct Option)

3 / 15

Conjugate of surd   a + \sqrt{b}    is _________

  • -a + \sqrt{b}
  • a - \sqrt{b}
  • \sqrt{a} + \sqrt{b}
  • \sqrt{a} - \sqrt{b}

(Select Correct Option)

4 / 15

The Degree of polynomial x^{2}y^{2} + 3 x y +y^{3} is _________

5 / 15

Order of Surd \sqrt[3]{x} is ________

6 / 15

(x+\frac{1}{x})^{2} = ................

  • x^{2}+\frac{1}{x^{2}}+2
  • x^{2}-\frac{1}{x^{2}}+2
  • x^{2}+\frac{1}{x^{2}}-2

(Select Correct Option)

7 / 15

\frac{a^{^{2}}-b^{2}}{a+b} is equal to __________

8 / 15

x²-4 =  ___________

9 / 15

"4x +3y -2" is an algebraic _____________

10 / 15

\frac{1}{a-b}-\frac{1}{a+b} is equal to ______

  • \frac{2a}{a^{2}-b^{2}}
  • \frac{2b}{a^{2}-b^{2}}
  • \frac{-2a}{a^{2}-b^{2}}
  • \frac{-2b}{a^{2}-b^{2}}

(Select Correct Option)

11 / 15

(3 + \sqrt{2}) (3 - \sqrt{2}) is equal to __________

12 / 15

2 (a^{2}+b^{2}) = (a+b)^{2} + (.............)^{^{2}}

13 / 15

(\sqrt{a}+\sqrt{b}) (\sqrt{a}-\sqrt{b}) is equal to __________

  • a^{2}+b^{2}
  • a^{2}-b^{2}
  • a-b
  • a+b

(Select Correct Option)

14 / 15

a^{3} + b^{3}   is equal to  ____________

 

15 / 15

\frac{1}{2-\sqrt{3}} = ...............

  • 2 - \sqrt{3}
  • 2 + \sqrt{3}
  • -2 - \sqrt{3}
  • -2 + \sqrt{3}

(Select Correct Option)

Your score is

Share  your Result with friends:

LinkedIn Facebook

You Can Follow eStudent.pk on

0%

Can u write your Feelings

How You Feel this

0%
0 votes, 0 avg
13

Revise / Test Your MCQs

Time is over

Thanks for taking Quiz, Click Finish Button to see your Result

Math Ch#16, 9th Class

Here MCQs for your Revision

For Good Revision & Grip on Concept, You Should take the MCQs and Revise it again and again

Good Luck. . . .  (:

Welcome

You Should Enter your Name

1 / 17

Area of a triangular region can be calculated as __________

2 / 17

Perpendicular distance between two parallel lines is _______ different.

3 / 17

The _____ of a triangle is the part of the plane enclosed by the triangle.

4 / 17

The unit of area is _____________

5 / 17

Congruent figures are ____ in area.

6 / 17

Parallelogram on equal and having the same / equal altitude are ____ in area.

7 / 17

Every diagonal of a parallelogram divides it in ____ congruent triangles.

8 / 17

A rectangular region can be divided in two or more rectangular region by ____ ways.

9 / 17

If a and b are length and breadth of a rectangle then its area is _______

10 / 17

A triangular region means the _____ of triangle and its interior.

11 / 17

Altitude of any triangle is perpendicular distance from _____ to opposite side.

12 / 17

Area of parallelogram is equal to the ____ of the base and height.

13 / 17

A quadrilateral having each angle 90 degree is called _____

14 / 17

The region enclosed by the bounding lines of a closed figure is called _______

15 / 17

Area of _______ is equal to = Base x Altitude

16 / 17

Any diagonal of a parallelogram divides it in two _____ triangles

17 / 17

Perpendicular from vertex of a angle to its opposite sides is called ______

Your score is

Share  your Result with friends:

LinkedIn Facebook

You Can Follow eStudent.pk on

0%

Can u write your Feelings

How You Feel this

0%
1 votes, 5 avg
117

Revise / Test Your MCQs

Time is over

Thanks for taking Quiz, Click Finish Button to see your Result

Math Ch#5, 09th Class

Here MCQs for your Revision

For Good Revision & Grip on Concept, You Should take the MCQs and Revise it again and again

Good Luck. . . .  (:

Welcome

You Should Enter your Name

1 / 15

Find m so that x^{2}+4x+m is a completed square_____

2 / 15

x^{2}+5x+6  can factorize as _____________

3 / 15

Factored form of x^{2}-16 is ___________

4 / 15

Factors of 5x^{2}-17xy-12y^{2} are _____

5 / 15

The Factors of x^{2} - 5x + 6 are_________

6 / 15

What will be added to complete the square of 9a^{2}-12ab _______

  • -16b^{2}
  • 16b^{2}
  • 4b^{2}
  • -4b^{2}

(Which Option is Correct)

7 / 15

Factors of 3x^{2}-x-2 are __________

8 / 15

Factors of 8x^{3} +27y^{3} are ___________

  • (2x+3y), (4x^{2}+9y^{2})
  • (2x-3y), (4x^{2}-9y^{2})
  • (2x+3y), (4x^{2}-6xy+9y^{2})
  • (2x-3y), (4x^{2}+6xy+9y^{2})

(Select Correct Option)

9 / 15

if x-2 is factor of    p(x) = x^{2}+2kx+8    , then k = _______

10 / 15

4a^{2}-16 can be factorize as __________

11 / 15

Factors of a^{4}-4b^{4} are _________

  • (a-b), (a+b), (a^{2}+4b^{2})
  • (a-b), (a+b), (a^{2}-4b^{2})
  • (a^{2}-2b^{2}), (a^{2}+2b^{2})
  • (a-2b), (a^{2}+2b^{2})

(Select Correct Option)

12 / 15

Factors of 27x^{2}-\frac{1}{x^{3}}  are ____________

  • \left ( 3x-\frac{1}{x} \right )\left ( 9x^{2}+3+\frac{1}{x^{2}} \right )
  • \left ( 3x+\frac{1}{x} \right )\left ( 9x^{2}+3+\frac{1}{x^{2}} \right )
  • \left ( 3x-\frac{1}{x} \right )\left ( 9x^{2}-3+\frac{1}{x^{2}} \right )
  • \left ( 3x+\frac{1}{x} \right )\left ( 9x^{2}-3+\frac{1}{x^{2}} \right )

(Select Correct Option)

13 / 15

(x+y)(x^{2}-xy+y^{2}) = ................

  • (x^{3}-y^{3})
  • (x^{3}+y^{3})
  • (x+y)^{3}
  • (x-y)^{3}

(Select Correct Option)

14 / 15

4a^{2}+4ab+(...........) is a complete square

  • b^{2}
  • 2b
  • ab

(Select Correct Option)

15 / 15

____________ =  \frac{x^{2}}{y^{2}}-2+\frac{y^{2}}{x^{2}}

  • \left ( \frac{x}{y} +\frac{y}{x}\right )^{2}
  • \left ( \frac{x}{y} -\frac{y}{x}\right )^{2}
  • \left ( \frac{y}{x} +\frac{x}{y}\right )^{2}

Your score is

Share  your Result with friends:

LinkedIn Facebook

You Can Follow eStudent.pk on

0%

Can u write your Feelings

How You Feel this

0%
0 votes, 0 avg
21

Revise / Test Your MCQs

Time is over

Thanks for taking Quiz, Click Finish Button to see your Result

Math Ch#14, 9th Class

Here MCQs for your Revision

For Good Revision & Grip on Concept, You Should take the MCQs and Revise it again and again

Good Luck. . . .  (:

Welcome

You Should Enter your Name

1 / 12

Equality of _____ ratio is defined as proportion.

2 / 12

The ratio between two quantities “a and b” is expressed as _______

3 / 12

One and only one line can be drawn through _____ points.

4 / 12

The line segment has only ___ point of bisection

5 / 12

If a : b=c : d then a, b, c and d are said to be in _____

6 / 12

________ has no unit.

7 / 12

Unit of ratio is __________

8 / 12

If adjacent angles of two intersecting lines are congruent then lines are ____ to each other.

9 / 12

______  points can be determine a line.

10 / 12

______ altitudes of equilateral triangle are congruent.

11 / 12

In two similar triangles, ______ sides are proportional

12 / 12

Symbol to show similarity is used ________

Your score is

Share  your Result with friends:

LinkedIn Facebook

You Can Follow eStudent.pk on

0%

Can u write your Feelings

How You Feel this