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This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 151. |
Using the figure, answer the following questions and justify your answer. (i) Is ∠1 adjacent to ∠2? (ii) Is ∠AOB adjacent to ∠BOE? (iii) Does ∠BOC and ∠BOD form a linear pair? (iv) Are the angles ∠COD and ∠BOD supplementary. (v) Is ∠3 vertically opposite to ∠1 ? |
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Answer» (i) Yes, ∠1 is adjacent to ∠2. Because they both have the common vertex ‘O’ and the common arm OA . Also their interiors do not overlap. (ii) No, ∠AOB and ∠BOB are not adjacent angles because they have overlapping interiors. (iii) No, ∠BOC and ∠BOD does not form a linear pair. Because ∠BOC itself a straight angle, so the sum of ∠BOC and ∠BOD exceed 180°. (iv) Yes, the angles ∠COD and ∠BOD are supplementary ∠COD + ∠BOD = 180°, [∵ linear pair of angles] ∴ ∠COD and ∠BOD are supplementary. (v) No. ∠3 and ∠1 are not formed by intersecting lines. So they are not vertically opposite angles. |
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| 152. |
Write a possible translation for each of chess piece for a single move. |
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Answer» Pawn – 1 ↑ or 2↑ Rook – 1 to 8 ↑ Knight – 2 → ,1 ↑ or 2 ← ,1 ↑ or 1 → ,2 ↑ or 1 ← ,2↑ Bishop – 1 → ,1 ↑ or 2 → ,2↑ or 3 → ,3↑ or 4 → ,4↑ or 5 → 5 ↑1 ← ,1↑ or 2 ← ,2↑ or 3 ← ,3↑ or 4 ← ,4↑ or 5 ← 5↑ Queen – 1 to 8 ,1 → , 1 ↑ or 2 → ,2↑ or 3 → ,3↑ or 4 → ,4↑ or 5 → ,5↑ or 1 ← ,↑1 or 2 ← ,2 ↑ or 3 ← ,3 ↑ or 4 ← ,4 ↑ or 5 ← 5↑ King – 1 → or ← or ↑ |
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| 153. |
In chess, a knight can move only in an L-shaped pattern:Two vertical squares, then one horizontal square;Two squares, then the one vertical square;One vertical square, then two horizontal sqaure; or One horizontal square, then two vertical square.Write a series of translations to move the knight from g8 to g5 (at most two moves) |
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Answer» 2 ← ,1↓ and then 1 ← , 2↓ (or) 2 ← , 1↓and then 1 ← ,2↓ |
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| 154. |
The pink shape is congruent to blue shape. Describe a sequence of transformations in which the blue shape is the image of pink shape. |
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Answer» (i) Translation 3 ← , 5↑ and 90° counter clockwise rotation about the green point and translates 5 ← , 2↓, (ii) Translation 2 ← 90° counter clockwise rotation about the green point and translates 2 ← , 2↓. |
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| 155. |
Referring the graphic given, answer the following questions. Each bar of the category is made up of boy-girl-boy unit,(i) Which categories show a boy- girl-boy unit that is translation within the bar? (ii) Which categories show a boy-girl-boy unit that is reflected within the bar? |
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Answer» (i) Essay Writing category shows translation (ii) Essay Writing and Mono Acting categories shows reflection |
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| 156. |
Describe the transformation involved in the following pair of figures (letters). Write translation, reflection or rotation. |
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Answer» (i) rotation (ii) reflection (iii) translation (iv) reflection (v) rotation (vi) reflection (vii) rotation (viii) translation |
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| 157. |
The transformation used in the picture is(i) Translation (ii) Rotation (iii) Reflection (iv) Glide Reflection |
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Answer» (i) Translation |
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| 158. |
The transformation used in the picture is(i) Translation (ii) Rotation (iii) Reflection (iv) Glide Reflection |
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Answer» (ii) Rotation |
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| 159. |
Given figure is a floor design in which the length of the small red equilateral triangle is 30 cm. All the triangles and hexagons are regular. Describe the translations in cm, represented by the (i) yellow line (ii) black line (iii) blue line. |
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Answer» (i) 120cm → , 210cm ↓ (ii) 270cm ← ,330cm ↑ (iii) 150 cm → |
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| 160. |
A __ is a flip over a line. (i) Translation (ii) Rotation (iii) Reflection (iv) Glide Reflection |
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Answer» (iii) Reflection |
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| 161. |
A __ is a slide; move without turning or flipping the shape. (i) Translation (ii) Rotation (iii) Reflection(iv) Glide Reflection |
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Answer» (i) Translation |
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| 162. |
A triangle has angle measurements of 29°, 65° and 86°. Then it is __ triangle. (i) an acute angled (ii) a right angled (iii) an obtuse angled (iv) a scalene |
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Answer» (i) an acute angled |
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| 163. |
Each angle of an equilateral triangle is of measure. |
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Answer» Each angle of an equilateral triangle is of measure same. |
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| 164. |
A point where two sides of a triangle meet is known as __ of a triangle. |
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Answer» A point where two sides of a triangle meet is known as vertese of a triangle. |
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| 165. |
A triangle has ___ vertices and ___ sides. |
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Answer» A triangle has three vertices and three sides. |
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| 166. |
Triangle is formed by joining three ___ points. |
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Answer» Triangle is formed by joining three non collinear points. |
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| 167. |
A triangle is formed by joining the mid- points of the sides of a given triangle. This process is continued indefinitely. All such triangles formd are similar to one another. (True/False). |
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Answer» Correct Answer - True N/A |
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| 168. |
In the given Fig. if AB = 2, BC = 6, AE = 6, BF = 8, CE = 7, and CF = 7, compute the ratio of the area of quadrilateral ABDE to the area of ACDF. |
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Answer» Given: AB = 2, BC = 6, AE = 6, BF = 8, CE = 7 and CF = 7 Consider ∆AEC and ∆BCF, In ∆AEC, AC = 8, AE = 6, CE = 7 In ∆BCF, BF = 8, BC = 6, CF = 7 ∴ ∆AEC ≅ ∆BCF ∴ Area of ∆AEC = Area of ∆BCF Subtract area of ∆BDC both sides, we get Area of ∆AEC – Area of ∆BDC = Area of ∆BCF – Area of ∆BDC ⇒ Area of quadrilateral ABDE = Area of ∆CDF ∴ The required ratio is 1 : 1 |
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| 169. |
In the following figure , `QS=x, SR=y, angle QPR=90^@ and angle PSR=90^@`, Find the `(PQ)^2=(PR)^2` interms of x and y. |
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Answer» Correct Answer - `x^2-y^2` N/A |
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| 170. |
In the given figure if ∠A = ∠C then prove that ∆AOB ~ ∆COD. |
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Answer» In triangles ∆AOB and ∆COD ∠A = ∠C (Y given) ∠AOB = ∠COD [∵ Vertically opposite angles] ∠ABO = ∠CDO [Remaining angles of ∆AOB and ∆COD] ∴ ∆AOB ~ ∆COD [∵ AAA similarity] ∵ ∆AOB ~ ∆COD [∵ AAA similarity] |
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| 171. |
The sum of the three angles of a triangle is ______ |
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Answer» The sum of the three angles of a triangle is 180°. |
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| 172. |
The exterior angle of a triangle is equal to the sum of the _______ angles opposite to it. |
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Answer» The exterior angle of a triangle is equal to the sum of the interior angles opposite to it. |
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| 173. |
The difference between any two sides of a triangle is _______ than the third side. |
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Answer» The difference between any two sides of a triangle is Smaller than the third side. |
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| 174. |
The angles of a triangle are in the ratio 4 : 5 : 6(i) Is it an acute, right or obtuse triangle?(ii) Is it scalene, isosceles or equilateral? |
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Answer» (i) Given the angles of a triangle are in the ratio 4 : 5 : 6 Sum of three angles of a triangle = 180°. Let the three angles 4x, 5x and 6x 4x + 5x + 6x = 180° 15x = 180° [∵ Vertically opposite angles are equal] ∴ x = 180°/15 ∴ x = 12° ∴ The angles are 4x ⇒ 4 × 12 = 48° 5x ⇒ 5 × 12 = 60° 6x ⇒ 6 × 12 = 72° ∴ The angle of the triangle are 48°, 60°, 72° ∴ It is an acute angles triangle. (ii) We know that the sides opposite to equal angles are equal. Here all the three angles are different. ∴ The sides also different. ∴ The triangle is a scalene triangle. |
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| 175. |
Angles opposite to equal sides are ______ and vice-versa. |
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Answer» Angles opposite to equal sides are Equal and vice-versa. |
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| 176. |
In the given figure, if ∆EAT ~ ∆BUN find the measure of all angles. |
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Answer» Given ∆EAT ≡ ∆BUN ∴ Corresponding angles are equal ∴ ∠E = ∠B ..(1) ∠A = ∠U ..(2) ∠T = ∠N ..(3) ∠E = x° ∠A = 2x° Sum of three angles of a triangle = 180° In ∆EAT, x + 2x + ∠T = 180° ∠T = 180° – (x° + 2x° ) ∠T = 180°- 3x° …(4) Also in ∆BUN (x + 40)° + + ∠U = 180° x + 40° + x + ∠U = 180° 2x° + 40° + ∠U = 180° ∠U = 180° – 2x – 40° = 140° – 2x° Now by (2) ∠A = ∠U 2x = 140° – 2x 2x + 2x = 140° 4x = 140° x = 140/4 = 35° ∠A = 2x° = 2 × 35° = 70° ∠N = x + 40° = 35° + 40° = 75° ∴ ∠T = ∠N = 75° ∠E = ∠B = 35° ∠A = ∠U = 70° |
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| 177. |
If the sides of a triangle are in the ratio 5:12:13 then, it is ……… |
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Answer» A right angled triangle. 132 = 169 52 = 25 122 = 144 169 = 25 + 144 132 = 52 + 122 By Pythagoras theorem, In a right triangle, square of the hypotenuse is equal to the sum of the squares of other two sides. |
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| 178. |
In Fig. 2.37, (a) name any four angles that appear to be acute angles. (b) name any two angles that appear to be obtuse angles. |
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Answer» (a) ∠AEB, ∠ADE, ∠BAE, ∠BCE (b) ∠BCD, ∠BAD |
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| 179. |
What is common in the following figures (i) and (ii) (Fig. 2.36.)?Is Fig. 2.36 (i) that of triangle? if not, why |
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Answer» Both figures have 3 line segments. No. It is not a closed figure |
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| 180. |
In which of the following figures (Fig. 2.35), (a) perpendicular bisector is shown? (b) bisector is shown? (c) only bisector is shown? (d) only perpendicular is shown? |
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Answer» The correct answer is (a) (ii) (b) (ii) and (iii) (c) (iii) (d) (i) |
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| 181. |
From the figures name pair of angles |
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Answer» (i) m and n are parallel lines and l is the transversal. ∴ ∠1 and ∠2 are exterior angles on the same side of the transversal. (ii) m and n are parallel lines and l is the transversal ∠1 and ∠2 are alternate exterior angles. (iii) m and n are parallel lines l is the transversal ∠1 and ∠2 are corresponding angles. (iv) m and n are parallel lines l is the transversal. ∠1 and ∠2 are interior angles on the same side of the transversal. (v) m and n are parallel lines and l is the transversal. ∠1 and ∠2 are alternate interior angles. (vi) o and q are parallel lines and n is the transversal. ∠1 and ∠2 are corresponding angles. |
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| 182. |
Find the measure of angle x in each of the following figures. |
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Answer» (i) m and n are parallel lines and l is the transversal. x° and 35° are corresponding angles and so they are equal. ∴ x = 35° (ii) m and n are parallel lines and l is the transversal. ∴ x = 65° [∴ corresponding angles are equal]. (iii) n and m are parallel lines and l is the transversal. Corresponding angles are equal ∴ x = 145° (iv) m and n are parallel lines and l is the transversal. Corresponding angles are equal ∴ x = 135° (v) m and n are parallel lines, l is the transversal perpendicular to both the lines ∴ x = 90° |
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| 183. |
Find the measure of angles in each of the following figures. |
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Answer» (i) m and n are parallel lines. l is the transversal. Then alternate interior angles are equal ∴ y = 28° (ii) m and n are parallel lines. l is the transversal. Alternate exterior angles are equal ∴ y = 58° (iii) m and n are parallel lines. l is the transversal. Alternate interior angles are equal ∴ y = 123° (iv) m and n are parallel lines. l is the transversal alternate exterior angles are equal. ∴ y = 108° |
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| 184. |
Pick out the Right angles from the given figures. |
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Answer» (i), (iii) and (v) are Right Angles. |
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| 185. |
Find the measure of angle z in each of the following figures. |
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Answer» (i) m and n are parallel lines l is the transversal Then interior angles that lie on the same side of the transversal are supplementary ∴ z + 31° = 180° z + 31° – 31° = 180° – 31° z = 149° (ii) m and n are parallel lines, l is the transversal Interior angles that lie on the same side of the transversal are supplementary ∴ z + 135° = 180° z + 135° – 135° = 180° – 135° z = 45° (iii) m and n are parallel lines l is the transversal exterior angles that lie on the same side of the transversal are supplementary. ∴ z + 79° = 80° z + 79° – 79° = 180° – 79° z = 101° (iv) m and n are parallel lines and l is the transversal. Corresponding angles are equal z + 22° = 180° z + 22° – 22° = 180° – 22° z = 158° |
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| 186. |
Pick out the Acute angles from the given figures. |
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Answer» (i), (iii) and (iv) are the Acute Angles. |
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| 187. |
Four real life examples of vertically opposite angles are given below. |
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Answer» (i) The four angles made in the scissors where the opposite angles are always equal. (ii) The point where two roads intersect each other. (iii) Rail road crossing signs. (iv) An hourglass. |
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| 188. |
Fill in the blanks.(a) Every triangle has at least _____ acute angles.(b) A triangle in which none of the sides equal is called a _____.(c) In an isosceles triangle ______ angles are equal.(d) The sum of three angles of a triangle is ______.(e) A right-angled triangle with two equal sides is called ______. |
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Answer» (a) Two (b) Scalene Triangle (c) Two (d) 180° (e) Isosceles right-angled triangle |
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| 189. |
Mention two real life situations where we use parallel lines. |
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Answer» Two angles of a wall in a building Cross rods in a window. |
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| 190. |
How many line segments are there in given figure? |
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Answer» Only one line segment, AB is there. |
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| 191. |
Anbu has marked the angles as shown below in (i) and (ii). Check whether both of them are correct. Give reasons |
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Answer» (i) m and n are parallel lines. l is the transversal. Interior angles on the same side of the transversal are supplementary. But here it is 75 + 75 ≠ 180° 105 + 105 ≠ 180° ∴ Angles marked are not correct (ii) m and n are parallel lines. l is the transversal. Corresponding angles must be equal. So here the marking is wrong. |
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| 192. |
In given figure, how many points are marked? Name them. |
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Answer» Three points A, B and C are marked. |
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| 193. |
In given figure, how many points are marked? Name them. |
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Answer» Four points A, B, C and D are marked. |
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| 194. |
In given figure how many line segments are there? Name them. |
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Answer» Six line segments, namely AB, AC, AD, BC, BD and CD. |
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| 195. |
How many line segments are there in given figure? Name them. |
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Answer» Three line segments, namely AB, BC and AC are there. |
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| 196. |
In given figure, how many points are marked? Name them. |
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Answer» Five points are marked, namely A, B, D, E and C. |
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| 197. |
In a right triangle ,one of the acute angles is four times the other. Find its measure.A. `68^(@)`B. `84^(@)`C. `80^(@)`D. `72^(@)` |
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Answer» Correct Answer - D Let the required measure be `x^(@)`. Measure of the other acute angle. `=((x)/(4))^(@)` `x^(@)+((x)/(4))^(@)+90^(@)=180^(@)` `x^(@)=72^(@)` Hence, the correct option is (d). |
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| 198. |
In given figure how many line segments are there? Name them. |
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Answer» Ten line segments, namely AB, AD, AE, AC, BD, BE, BC, DE, DC and EC. |
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| 199. |
Write the name of (a) vertices (b) edges, and (c) faces of the prism shown in Fig. 2.48. |
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Answer» (a) Vertices A, B, C, D, E, F (b) Edges AB, AC, BC, BD, DF, FC, EF, ED, AE (c) Faces ABC, DEF, AEFC, AEDB, BDFC |
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| 200. |
Can we have two acute angles whose sum is(a) an acute angle? Why or why not?(b) a right angle? Why or why not?(c) an obtuse angle? Why or why not?(d) a straight angle? Why or why not?(e) a reflex angle? Why or why not? |
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Answer» (a) Yes, ∵ the sum of two acute angles can be the acute angle. E.g„ 30° and 40° are two acute angles and their sum = 30° + 40° = 70°, which is also an acute angle. (b) Yes, ∵ the sum of two acute angles can be a right angle. E.g., 30° and 60° are two acute angles and their sum = 30° + 60° = 90°, which is a right angle. (c) Yes, ∵ the sum of two acute angles can be an obtuse angle. E.g., 45° and 60° are two acute angles and their sum = 45° + 60° = 105°, which is an obtuse angle. (d) No, ∵ the sum of two acute angles is always less than 180°. (e) No, ∵ the sum of two acute angles is always less than 180°. |
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