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Ask QuestionPosted by Jeevitha R 3 years, 11 months ago
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Unknown . 3 years, 11 months ago
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Posted by Deepika Sharma 3 years, 11 months ago
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Yogita Ingle 3 years, 11 months ago
In two triangles ABC and DEF , AB = DE, BC=DF and AC=EF then (a)∆ABC≅∆DEF (b)∆ABC≅∆FED (c)∆ABC≅∆EDF (d)None of these
Answer:
AB = DE
BC=DF
AC=EF
∆ABC≅∆DEF
Posted by M Nagaraj Nagaraj 3 years, 11 months ago
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Yogita Ingle 3 years, 11 months ago
Given : A parallelogram ABCD , in which AC = BD
TO Prove : ABCD is a rectangle .
Proof : In △ABC and △ABD
AB = AB [common]
AC = BD [given]
BC = AD [opp . sides of a | | gm]
⇒ △ABC ≅ △BAD [ by SSS congruence axiom]
⇒ ∠ABC = △BAD [c.p.c.t.]
Also, ∠ABC + ∠BAD = 180° [co - interior angles]
⇒ ∠ABC + ∠ABC = 180° [∵ ∠ABC = ∠BAD]
⇒ 2∠ABC = 180°
⇒ ∠ABC = 1 /2 × 180° = 90°
Hence, parallelogram ABCD is a rectangle.
Posted by Nishu Yadav 3 years, 11 months ago
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Posted by Ritika Jangra 3 years, 11 months ago
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Posted by Jeff Musk 3 years, 11 months ago
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Gaurav Seth 3 years, 11 months ago
Theorem 6. 1 : If two lines intersect each other, then the vertically opposite angles are equal
Given :- two lines intersect each other
To prove :- ∠AOC = ∠BOD and ∠AOD = ∠BOC
Proof :- AB and CD be two lines intersecting at O as shown in Fig 6 8 They lead to two pairs of
vertically opposite angles, namely, (i) ∠AOC and ∠ BOD
(ii) ∠ AOD and ∠ BOC
We need to prove that ∠AOC = ∠BOD
and ∠AOD = ∠BOC
Now, ray OA stands on line CD
From (Linear pair axiom)
∠AOC + ∠AOD = 180° … (1)
∠AOD + ∠BOD = 180° … (2)
From (1) and (2), we can write
∠AOC + ∠AOD = ∠AOD + ∠BOD
This implies that ∠AOC = ∠BOD
Similarly, it can be proved that ∠AOD = ∠BOC
Parallel Lines and a Transversal
∠1, ∠ 2, ∠7 and ∠ 8 are called exterior angles,
∠ 3, ∠ 4, ∠ 5 and ∠6 are called interior angles
(a) Corresponding angles :
(i) ∠1 = ∠ 5 (ii) ∠ 2 = ∠ 6 (iii) ∠ 4 = ∠ 8 (iv) ∠ 3 = ∠ 7
(b) Alternate interior angles :
(i) ∠ 4 = ∠ 6 (ii) ∠ 3 = ∠ 5
(c) Alternate exterior angles:
(i) ∠1 = ∠ 7 (ii) ∠ 2 = ∠8
(d) Interior angles on the same side of the transversal:
(i) ∠4 + ∠5 =180°(ii) ∠3 + ∠ 6 =180°
Posted by Ritika Jangra 3 years, 11 months ago
- 4 answers
Posted by Alisha Taneja 3 years, 11 months ago
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Yogita Ingle 3 years, 11 months ago
1) Mean = sum of all observation/ Total number of observation
Total Students = 15
Value of observation= 41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60
Mean =
Median:
1) Arrange data in ascending order
39,40,40,41,42,46,48,52,52,52,54,60,62,96,98
2) Total numbers of observation= 15
Odd: (n+1)/2
=(15+1)/2 = 8 th element is median
Median = 52
Mode:
1) Arrange data in ascending order
39,40,40,41,42,46,48,52,52,52,54,60,62,96,98
2) Count the frequency of each observation,the observation having most frequency is the mode
So, 52 appears 3 time,maximum time
Mode = 52
Posted by Jay Hanuman 3 years, 11 months ago
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Priyam Jain 3 years, 11 months ago
Posted by Tidke Pranav 3 years, 11 months ago
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Gaurav Seth 3 years, 11 months ago
Given: ABCD is a parallelogram. AC is a diagonal of parallelogram ABCD which divides it into two triangles, namely, ∆ABC and ∆CDA.
To Prove: ∆ABC ≅ ∆CDA
Proof: BC || DA
| Opposite sides of a parallelogram are parallel
and AC is a transversal
∴ ∠BCA = ∠DAC ...(1)
| Pair of alternate interior angles
Also, AB || DC
Opposite sides of a parallelogram are parallel
and AC is a transversal
∴ ∠BAC = ∠DCA ...(2)
| Pair of alternate interior angles
AC = CA ...(3) | Common
In view of (1), (2) and (3),
∆ABC ≅ ∆CDA
| ASA congruence criterion
Posted by Abhinandan? Dubey?? 3 years, 11 months ago
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Posted by Vanshika Dawar 3 years, 11 months ago
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Gaurav Seth 3 years, 11 months ago
Radius of the roller (r) = 84/ 2 cm = 42 cm
Length of the roller (h) = 120 cm
Curved surface area of the roller = 2πrh
= 2 × 22/ 7 × 42 × 120 cm2 = 44 × 720 cm2 = 31680 cm2
∴ area covered by the roller in 1 revolution = 31680 cm2
∴ area covered by the roller in 500 revolutions = 31680 × 500 cm2 = 15840000 cm
Hence, area of the playground = 15840000/ 100× 100 m2 = 1584 m2 Ans.
Posted by Namrata Singh 3 years, 11 months ago
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Posted by Ananya Vijayan 3 years, 11 months ago
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Gaurav Seth 3 years, 11 months ago
Shikha folded the three corners of a triangle. She managed to measure four of the angles as shown below before breaking her protractor. Help her to find f. g and h respectively. 89 A. 520, 440, 47° B44 520 47° C. 48°, 47, 54° D. 84°, 47°, 480
Answer
The value of g=360°-(130°+94°+84°) as they're in a quadrilateral.
g=52°.
The only choice corresponding to this is b.
Hence (b) is the correct answer.
Posted by Ishika Kumari 3 years, 11 months ago
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Yogita Ingle 3 years, 11 months ago
Given, Perimeter of rhombus =40cm
All sides of rhombus are equal, hence, side, a= 40/4 =10cm
Diagonal of rhombus, p=12cm
Area of rhombus =1/2 p √4a2−p2
Area of rhombus =1/2 (12)√4(10)2−122
Area of rhombus =96 cm2
Total area of both the sides = 2 × 96=192cm2
Cost of painting 1cm2 = Rs. 5
Cost of painting 192cm2 = 192 × 5= Rs. 960
Posted by Rishabh Yadav 3 years, 11 months ago
- 5 answers
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Sahil Nara 3 years, 11 months ago
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