Discussion
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- Question
- If ABCD is a parallelogram and AC and BD be its diagonals, then:
Options- A. AB2 + BC2+ CD2+ DA2 = AC2 ? BD2
- B. AB2 + BC2+ CD2 + DA2 = AC2 + BD2
- C. 4AD2 = 2AC2 + 2BD2
- D. 4AB2 = 2AC2 ? 2BC2
- Correct Answer
- AB2 + BC2+ CD2 + DA2 = AC2 + BD2
ExplanationIn ||gm ABCD , we have
Since diagonals of parallelogram(||gm ) bisect each other,
? M will be the mid-point of each of the diagonal AC and BD
? In ?ABC AB2 + BC2 = 2(AM2 + MB2) ......... ( 1 ) [Appolonius Theorem]
In ?ADC AD2 + CD2 = 2(AM2 + DM2) ......... ( 2 )
= 2(AM2 + MB2) [? DM = BM]
Adding equations ( 1 ) and ( 2 )
AB2 + BC2 + CD2 + DA2 = 2(AM2 + MB2 + 2(AM2 + MB2 = 4AM2 + 4MB2
= (2AM)2 + (2MB)2= AC2+ BD2. { ? AM = MC , MB = MD } - 1. In a right angled ? ABC, Right angled at A, AD ? BC. Then :
Options- A. AD2 = BD × CD
- B. AD2 = AB × AC
- C. AD2 = BD × AB
- D. AD2 = CD × AC Discuss
- 2. A vertical stick 12 cm long casts a shadow 8 cm long on the ground. At the same time a tower casts the shadow 40 m long on the ground. Find the height of the tower.
Options- A. 600 m
- B. 160 m
- C. 60 m
- D. 52 m Discuss
- 3. In, ?ABC, D and E are the mid-points of AB and AC respectively. Find the ratio of the areas of ?ADE and ?ABC.
Options- A. 1 2
- B. 1 4
- C. 3 4
- D. 1 8 Discuss
- 4. In the given figure, find the length of BD.
Options- A. 13.5 cm
- B. 12 cm
- C. 14.5 cm
- D. 15 cm Discuss
- 5. In the given figure ?QPR = 90°, QR = 26 cm, PM = 6 cm, MR = 8 cm and ?PMR = 90°, find the area of ?PQR.
Options- A. 180 cm2
- B. 240 cm2
- C. 120 cm2
- D. 150 cm2 Discuss
- 6. In the given figure, DE || BC and DE : BC = 3 : 5 the ratio of the areas of ? ADE and the trapezium BCED.
Options- A. 9 25
- B. 12 25
- C. 3 4
- D. 9 16 Discuss
- 7. In a ? ABC, AD intersects ? A and BC. If BC = a, AC = b and AB = c, Then :
Options- A. CD = b+c ab
- B. CD = ab b+c
- C. CD = bc+ab ac
- D. CD = ac cb+ab Discuss
- 8. In the given figure DE||BC and AD : DB = 5 : 4,
Then ar(?DFE) ar(?CFB)
Options- A. 25 81
- B. 25 16
- C. 16 25
- D. 16 81 Discuss
- 9. In center of a triangle lies in the interior of :
Options- A. an isosceles triangle only
- B. any triangle
- C. an equilateral triangle only
- D. a right triangle only Discuss
- 10. In the given figure, which of the following is true :
Options- A. x = ? + ? + ?
- B. x + ? = ? + ?
- C. x + ? = ? + ?
- D. x + ? = ? + ? Discuss
Plane Geometry problems
Search Results
Correct Answer: AD2 = BD × CD
Explanation:
Correct Answer: 60 m
Explanation:
Correct Answer: 1 4
Explanation:
Correct Answer: 13.5 cm
Explanation:
Correct Answer: 120 cm2
Explanation:
Given in the question, QR = 26 cm, PM = 6 cm, MR = 8 cm
According to question, in ? PMR
(Pythagoras Theorem)
PR = ?PM2 + MR2 = ?36 + 64 = ? 100 = 10 cm
According to question, in ? PQR
(Pythagoras Theorem)
PQ = ?QR2 - PR2 = ?262 - 102 = ?576 - 100 = ? 476 = 24
? area of triangle ?PQR = Base length x Height / 2
? area of triangle ?PQR = PR x PQ / 2
? area of triangle ?PQR = 10 x 24 / 2 = 10 x 12
? area of triangle ?PQR = 120
Correct Answer: 9 16
Explanation:
Correct Answer: CD = ab b+c
Explanation:
Correct Answer: 25 81
Explanation:
Correct Answer: any triangle
Explanation:
We know that In center of every triangle ( acute , obtuse and right angle ) lies in its interior.
Hence required answer will be any triangle .
Correct Answer: x = ? + ? + ?
Explanation:
From above figure , we can see that
Join B and D and produce BD to E
Then, p + q = ? and s + t = x
We know that , Exterior angle = Sum of two interior angle
Now, s = p + ? (Exterior angle of a ? prop.)
Similarly, t = q + ? (Exterior angle of a ? prop.)
Adding, s + t = p + q + ? + ?
Putting s + t = x and p + q = ? ,
Hence x = ? + ? + ?
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