 # Geometry Exam Preparation

### General Exam Preparation tips to consider:

• After COVID-19 writing speed as well as focus has affected a lot.
• A lot of writing practice that has to be done by you.
• You must keep a track of your time while solving your mock papers and at the same time try to finish your exam at least 15 minutes early.
• Make sure that your presentation is neat and tidy.
• The question as well as answers should be in the same order for the examiner’s convenience. Note: If your Examiner is happy and can understand what you have written you have won half the battle.
• Learn the High Weighted Chapters First
• Study with the help of Small Goals and reward yourself for the same.
• Make sure to solve mock question papers you will know more clearly about exam pattern, marking structure, as well as important questions.

### Chapter Wise Important formulas/theorems for geometry exam

#### Chapter 1 Similarity:

In this chapter you will learn the major properties of triangles.

• Property 1 : The ratio of areas of two triangles is equal to the ratio of the product of their bases and corresponding heights.
• Property 2 : The ratio of areas of two triangles with equal height is equal to the ratio of their corresponding bases
• Property 3 : The ratio of areas of two triangles having equal bases, is equal to the ratio of their corresponding heights.
• Property 4 : Areas of two triangles having equal bases and equal heights are equal.

Basic Proportionality  Theorem (B. P. T.):  If a line parallel to a side of a  triangle intersects the  remaining sides in two distinct points, then the line divides those sides in the same proportion.

Property of an Angle Bisector of a Triangle Statement : In a triangle, the angle bisector divides the side opposite to the angle in the ratio of the remaining sides. Furthermore, you will learn the various similarity tests of triangles such as A-A-A test, S-A-S test, S-A-S test.

Theorem of Areas of Similar Triangles: The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.

#### Chapter 2 Pythagoras Theorem

Similarity and Right Angled Triangles : ‘In a right angled triangle, if the altitude is drawn from the vertex of the right angle to the hypotenuse,then the two triangles formed are similar to the original triangle and to each other’.

Theorem of Geometric Mean : ‘In a right angled triangle, the length of the perpendicular segment drawn on the hypotenuse from the opposite vertex, is the geometric mean of the segments into which the hypotenuse is divided’.

Theorem of Pythagoras : Statement : ‘In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the remaining two sides’.

Converse of Pythagoras theorem : Statement : In a triangle, if the square of one side is equal to the sum of the squares of remaining two sides, then the angle opposite to the first side is a right angle and the triangle is right angled triangle.

#### Chapter 3 Circle:

In this chapter you will learn the basics of circle like Radius, diameter, tangent, secant.

Tangent theorem : A tangent at any point of a circle is perpendicular to the radius, through the  point of contact.

Converse of tangent theorem : A line perpendicular to a radius of a circle at its outer end is a tangent to the circle.

Tangent segment Theorem : The lengths of the two tangent segments to a circle drawn from an external point are equal. Moreover, types of Arc like minor Arc, major arc and semicircle.

Inscribed Angle Theorem: The measure of an inscribed angle is half of the measure of its intercepted arc.

Cyclic Quadrilateral theorem: The opposite angles of a cyclic quadrilateral are supplementary.

Converse of cyclic quadrilateral theorem : If the opposite angles of a quadrilateral are supplementary, then it is a cyclic quadrilateral.

Tangent Secant Theorem: If an angle with its vertex on the circle whose one side touches the circle and the other intersects the circle in two points, then the measure of the angle is half the measure of its intercepted arc.

#### Chapter 4 Geometric Constructions

In this chapter you will learn the various methods of Geometric Constructions right from basic construction like angle bisector, perpendicular bisector to the construction of similar triangles when both triangles do not have a common angle and have a common angle. Furthermore, Construction of a tangent to the circle from a point on the circle without using the centre and with using a centre and point outside the circle.

#### Chapter 5 Co-ordinate Geometry:

Distance Formula : If A (x1, y1) and (x2, y2) are two points, then distance between these points is given by the following formula : d(A, B) = √(x2-x1)² (y2-y1)²

Section formula for division of a line segment : If P(x, y) divides segment joining A(x1, y1) and B(x2, y2) in the ratio m : n, then x= mx2+nx1/m+n  and y= my2+ny1/m+n

Midpoint formula: If M(x, y) is the midpoint of segment joining A(x1, y1) and B(x2, y2), then and If point P is the midpoint of segment AB andP(x, y), A(x1, y1), B(x2, y2) then m = n and values of x and y can be written as x= x1+x2/2 and y= y1+y2/2.

Centroid formula: Co-ordinates of centroid of a triangle whose vertices are (x1, y1), (x2, y2) and (x3, y3) are  {(x1+x2+x3/3), (y1+y2+y3/3)}.

Slope of Line Using inclination: Inclination of a line Angle formed by a line with positive X-axis is  called inclination of a line. It is represented by ‘θ’ Slope of a line = tan θ.

#### Chapter 6 Trigonometry

Trigonometry deals with measurements of sides as well as angles of a right angled triangle. Don’t forget to learn this table, this is where your entire chapter sums up.

#### Chapter 7 Menstruation:

Mensuration is a special branch of mathematics that deals with the measurement of geometric figures. Furthermore, the important formulas are mentioned below which will help you score good in your Geometry exam

### Do’s and Don’ts of Studying Geometry for Board Exams:

• For CBSE STSolve each and every question of NCERT : 70% to 80% questions asked are directly from NCERT.
• Questions will have 4 sections and total number of questions will be 30 thus students need to be ready for short and long questions both.
• Board will ask you tricky questions, so focus on practising more of the sums.
• Make a Separate Note while revising your topics.
• Solve the Easier Questions First.
• Don’t forget to use the Units and Decimal Points wherever necessary, one single mistake can cost you your marks.
• Provide Diagram Wherever Necessary
• Practice case study questions majorly from all the chapters but pay special attention to the chapters like Arithmetic Progression, Surface Areas & Volumes, Trigonometry.
• Keep your Exam paper neat and clean, avoid overwriting and more cuttings.
• Make sure your rough work is neat and clean.
• Your basics should be clear and you should continuously practise as well brush up the concepts.
• Try to do Group studies you will practise more as well as get a more detailed solution along with fun.
• Note down all the formulas in a book
• Be well versed with all the basics of Trigonometry and Menstruation.

### Important formulas to study for geometry exam:

#### Trigonometry:

1. sin(90° – A) = cos A
2. cos(90° – A) = sin A
3. tan(90° – A) = cot A
4. cot(90° – A) = tan A
5. sec(90° – A) = cosec A
6. cosec(90° – A) = sec A
7. sin2 θ + cos2 θ = 1 ⇒ sin2 θ = 1 – cos2 θ ⇒ cos2 θ = 1 – sin2 θ
8. cosec2 θ – cot2 θ = 1 ⇒ cosec2 θ = 1 + cot2 θ ⇒ cot2 θ = cosec2 θ – 1
9. sec2 θ – tan2 θ = 1 ⇒ sec2 θ = 1 + tan2 θ ⇒ tan2 θ = sec2 θ – 1
10. sin θ cosec θ = 1 ⇒ cos θ sec θ = 1 ⇒ tan θ cot θ = 1

#### Circle:

• The tangent to a circle equation x2 + y2 = a2 for a line y = mx + c is given by the equation y = mx ± a √[1+ m2].
• The tangent to a circle equation x2 + y2 = a2 at (a1,b1) is xa1 + yb1 = a2

#### Surface area and Volume Formula:

1. Volume Of Sphere = 4/3 ×π r3
2. Lateral Surface Area of Sphere (LSA) = 4π r2
3. Total Surface Area of Sphere (TSA) = 4πr2
4. Volume of Right Circular Cylinder = πr2h
5. Lateral Surface Area of Right Circular Cylinder (LSA) = 2×(πrh)
6. Total Surface Area of Right Circular Cylinder (TSA) = 2πr×(r + h)
7. Volume of Hemisphere = ⅔ x (πr3)
8. Lateral Surface Area of Hemisphere (LSA) = 2πr2
9. Total Surface Area of Hemisphere (TSA) = 3πr2
10. Volume of Prism = B × h
11. Lateral Surface Area of Prism (LSA) = p × h
12. Total surface area of a cuboid = 2 (lb + bh + lh)
13. Lateral surface area of a cuboid = 2 (l + b) × h
14. Volume of a cuboid = l × b × h
15. Diagonal of the cuboid = √l²+b²+h²
16. Total surface area of a cube = 6l²
17. Lateral surface area of a cube = 4l²
18. Volume of cube = l³
19. Diagonal of the cube = √3l
20. Curved surface area of a right circular cone = πrl
21. Total surface area of a right circular cone = πr (r +l)
22. Volume of a right circular cone = 1/3× πr²h

### Last Minute Exam Preparation Tips to Score Good marks.

• Get up early and use that time to study important topics
• Share problems you are facing and look for solutions
• Review the summaries you have rather than the entire chapters
• Reduce your Screen Time avoid using Technology
• Consider taking breaks, refresh yourself and start again.
• Get everything ready and in place for the next day
• Give more focus on your weak points
• Solve Mock papers
• Have a clear overview of your Exam

To conclude, Class 10 students should follow a schedule so that they can give equal time for all the chapters for their subjects. Hope you have noted the Important formulas and theorems to succeed in your geometry exam