allsolution

Risks To laugh is to risk appearing the fool. To weep is to risk appearing sentimental. To reach out to another is to risk involvement. To expose feelings is to risk exposing your true self. To place your dreams, ideas before a crowd is to risk their loss. To love is risk not being loved in return. To live is to risk dying. To hope is to risk despair. To try is to risk failure. But risks must be taken, because the greatest hazard in life is to risk nothing. The person who risks nothing, does nothing,  has nothing, and is nothing. They may avoid suffering and sorrow, but they cannot learn, feel, change, grow, love, live. Chained by their certitudes, they are a slave: they have  forfeited their freedom. Only a person who risks is truly free. RISKS To laugh is to risk appearing the fool.

Risks To laugh is to risk appearing the fool. To weep is to risk appearing sentimental. To reach out to another is to risk involvement. To expose feelings is to risk exposing your true self. To place your dreams, ideas before a crowd is to risk their loss. To love is risk not being loved in return. To live is to risk dying. To hope is to risk despair. To try is to risk failure. But risks must be taken, because the greatest hazard in life is to risk nothing. The person who risks nothing, does nothing,  has nothing, and is nothing. They may avoid suffering and sorrow, but they cannot learn, feel, change, grow, love, live. Chained by their certitudes, they are a slave: they have  forfeited their freedom. Only a person who risks is truly free. RISKS To laugh is to risk appearing the fool.

गाय हमारी माता हे। यह एक महत्वपूर्ण घरेलू जानवर है यह हमें स्वस्थ और पौष्टिक दूध देता है यह एक पालतू जानवर है यह एक जंगली जानवर नहीं है और दुनिया के कई हिस्सों में पाया जाता है। भारतीय लोग इसे एक माँ की तरह सम्मान करते हैं भारत में गाय की प्राचीन काल से देवी के रूप में पूजा की गई है। भारत में लोग अपने घरों में धन लक्ष्मी के रूप में लाते हैं। गाय को सभी जानवरों में एक पवित्र जानवर माना जाता है। यह विभिन्न आकार, रंग और कई किस्मों में पाया जाता है।   गाय बहुत उपयोगी पशु है और हमें दूध देता है गाय का दूध पूर्ण और पौष्टिक भोजन के रूप में जाना जाता है। गाय एक घरेलू और धार्मिक जानवर है भारत में गाय की पूजा हिंदू धर्म में एक कस्टम है गाय का दूध पूजा, अभिषेक और अन्य पवित्र कार्यों में प्रयोग किया जाता है। हिंदू धर्म में इसे "गाय मां" कहा जाता है और मां की जगह रखती है। यह एक बड़ा शरीर, चार पैर, एक लंबी पूंछ, दो सींग, दो कान, दो आँखें, एक बड़ा नाक, एक बड़ा मुंह और एक सिर जानवर है। यह देश के लगभग हर क्षेत्र में पाया जाता है। गाय हमारी मां की तरह है और दिन में दो बार दूध देता है। यह...

Essay on cow The cow is our mother. This is an important domestic animal. It gives us healthy and nutritious milk. This is a pet. It is not a wild animal and is found in many parts of the world. Indian people respect it like a mother. Cow in India has been worshiped in the form of Goddess from ancient times. People in India bring it in their homes as Dhan Lakshmi. The cow is considered as a sacred animal in all animals. It is found in different sizes, colors and many varieties. The cow is very useful animal and gives us milk. The cow’s milk is known as full and nutritious food. The cow is a domestic and religious animal. Cow worship in India is a custom in Hinduism. Cow’s milk is used in pooja, abhishek and other sacred works. In Hinduism it is called “cow mother” and keeps mother’s place. It is a large body, four legs, a long tail, two horns, two ears, two eyes, a big nose, a big mouth and a head animal. It is found in almost every region of the country. The cow is like ...

Q5 : Explain why a rectangle is a convex quadrilateral. Answer : In a rectangle, there are two diagonals, both lying in the interior of the rectangle. Hence, it is a convex quadrilateral.

Q10 : Explain how this figure is a trapezium. Which of its two sides are parallel Answer : If a transversal line is intersecting two given lines such that the sum of the measures of the angles on the same side of transversal is 180º, then the given two lines will be parallel to each other. Here, ∠ NML + ∠ MLK = 180° Hence,NM||LK As quadrilateral KLMN has a pair of parallel lines, therefore, it is a trapezium.

Q9 : In the above figure both RISK and CLUE are parallelograms. Find the value of x. Answer : Adjacent angles of a parallelogram are supplementary. In parallelogram RISK, ∠ RKS + ∠ ISK = 180° 120° + ∠ ISK = 180° ∠ ISK = 60° Also, opposite angles of a parallelogram are equal. In parallelogram CLUE, ∠ ULC = ∠ CEU = 70° The sum of the measures of all the interior angles of a triangle is 180º. x + 60° + 70° = 180° x = 50° https://Mungyo-Calligraphy-pen-assorted-colours/dp/B01KP59RKI?channel=dynmobile&placement=&target=boomuserlist%3A%3A456030001&campaignid=750806307&tag=http://notesjobs.blogspot.in/?m=1googinremarketing54-21

Q8 : The following figures GUNS and RUNS are parallelograms. Find x and y. (Lengths are in cm) Answer : (i)We know that the lengths of opposite sides of a parallelogram are equal to each other. GU = SN 3y - 1 = 26 3y = 27 y = 9 SG = NU 3x = 18 x = 6 Hence, the measures of x and y are 6 cm and 9 cm respectively. (ii)We know that the diagonals of a parallelogram bisect each other. y + 7 = 20 y = 13 x + y = 16 x + 13 = 16 x = 3 Hence, the measures of x and y are 3 cm and 13 cm respectively.

Q7 : The adjacent figure HOPE is a parallelogram. Find the angle measures x, y and z. State the properties you use to find them. Answer : y = 40° (Alternate interior angles) 70° = z + 40º (Corresponding angles) 70° - 40° = z z = 30° x + (z + 40º) = 180° (Adjacent pair of angles) x + 70º = 180° x = 110°

Q6 : Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram. Answer : Sum of adjacent angles = 180° ∠ A + ∠ B = 180º 2∠ A = 180º (∠ A = ∠ B) ∠ A = 90º ∠ B = ∠ A = 90º ∠ C = ∠ A = 90º (Opposite angles) ∠ D = ∠ B = 90º (Opposite angles) Thus, each angle of the parallelogram measures 90º.

Q5 : The measures of two adjacent angles of a parallelogram are in the ratio 3:2. Find the measure of each of the angles of the parallelogram. Answer : Let the measures of two adjacent angles, ∠A and ∠B, of parallelogram ABCD are in the ratio of 3:2. Let ∠A = 3x and ∠B = 2x We know that the sum of the measures of adjacent angles is 180 º for a parallelogram. ∠A + ∠B = 180 º 3x + 2x = 180 º 5x = 180 º X=180/5=36 ∠A = ∠C = 3x = 108 º (Opposite angles) ∠B = ∠D = 2x = 72 º (Opposite angles) Thus, the measures of the angles of the parallelogram are 108 º, 72 º, 108 º, and 72 º.

Q4 : Draw a rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measure. Answer : Here, quadrilateral ABCD (kite) has two of its interior angles, ∠ B and ∠ D, of same measures. However, still the quadrilateral ABCD is not a parallelogram as the measures of the remaining pair of opposite angles, ∠ A and ∠ C, are not equal.

Q3 : Can a quadrilateral ABCD be a parallelogram if (i) ∠ D + ∠ B = 180° (ii) AB = DC = 8 cm, AD = 4 cm and BC = 4.4 cm (iii) ∠ A = 70° and ∠ C = 65° Answer : (i) For ∠ D + ∠ B = 180°, quadrilateral ABCD may or may not be a parallelogram. Along with this condition, the following conditions should also be fulfilled. The sum of the measures of adjacent angles should be 180º. Opposite angles should also be of same measures. (ii) No. Opposite sides AD and BC are of different lengths. (iii) No. Opposite angles A and C have different measures.

Q6 : (a) What is the minimum interior angle possible for a regular polygon (b) What is the maximum exterior angle possible for a regular polygon Answer : Consider a regular polygon having the lowest possible number of sides (i.e., an equilateral triangle). The exterior angle of this triangle will be the maximum exterior angle possible for any regular polygon. Exterior angle of an equilateral triangle Hence,     360/3= 120 maximum possible measure of exterior angle for any polygon is 120 º. Also, we know that an exterior angle and an interior angle are always in a linear pair. Hence, minimum interior angle = 180 º - 120° = 60 º

Q5 : (a) Is it possible to have a regular polygon with measure of each exterior angle as 22° (b) Can it be an interior angle of a regular polygon Why Answer : The sum of all exterior angles of all polygons is 360º. Also, in a regular polygon, each exterior angle is of the same measure. Hence, if 360º is a perfect multiple of the given exterior angle, then the given polygon will be possible. (a) Exterior angle = 22° 360º is not a perfect multiple of 22º. Hence, such polygon is not possible. (b) Interior angle = 22° Exterior angle = 180° - 22° = 158°

Exercise 3.2 Q.no.4 Q4 : How many sides does a regular polygon have if each of its interior angles is 165° Answer : Measure of each interior angle = 165° Measure of each exterior angle = 180° - 165° = 15° The sum of all exterior angles of any polygon is 360 º. Thus, number of sides of the polygon

Excerice 3.2 Q.no.3 Q3 : How many sides does a regular polygon have if the measure of an exterior angle is 24° Answer : Sum of all exterior angles of the given polygon = 360 º Measure of each exterior angle = 24 º Thus, number of sides of the regular polygon

Q2 : Find the measure of each exterior angle of a regular polygon of (i) 9 sides (ii) 15 sides Answer : (i) Sum of all exterior angles of the given polygon = 360 º Each exterior angle of a regular polygon has the same measure. Thus, measure of each exterior angle of a regular polygon of 9 sides = 360/9  = 40 (ii) Sum of all exterior angles of the given polygon = 360 º Each exterior angle of a regular polygon has the same measure. Thus, measure of each exterior angle of a regular polygon of 15 sides =360/15  = 24

Exercise 3.2 : Solutions of Questions on Page Number : 44 Q1 : Find x in the following figures. Figure (a) and (b) is in your book Answer : We know that the sum of all exterior angles of any polygon is 360º. (a) 125° + 125° + x = 360° 250° + x = 360° x = 110° (b) 60° + 90° + 70° + x + 90° = 360° 310° + x = 360° x = 50°