Discussion
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- Question
- In the given figure, find the length of BD.
Options- A. 13.5 cm
- B. 12 cm
- C. 14.5 cm
- D. 15 cm
- Correct Answer
- 13.5 cm
Explanation
- 1. 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
- 2. In the given figure, AM ? BC and AN is the bisector of ?A. What is the measure of ?MAN.
Options- A. 17.5°
- B. 15.5°
- C. 20°
- D. 25° Discuss
- 3. In the given figure, ?B = ?C = 55° and ?D = 25°. Then:
Options- A. BC < CA < CD
- B. BC > CA > CD
- C. BC < CA, CA > CD
- D. BC > CA, CA < CD Discuss
- 4. If two parallel lines are intersected by a transversal, then the bisectors of the two pairs of interior angles enclose a:
Options- A. Trapezium
- B. Rectangle
- C. Square
- D. circle Discuss
- 5. In the given figure, OP bisect ?BOC and OQ bisects ?AOC. Then ?POQ is equal to :
Options- A. 90°
- B. 120°
- C. 60°
- D. 100° Discuss
- 6. 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
- 7. 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
- 8. 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
- 9. 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 Discuss
- 10. 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
Plane Geometry problems
Search Results
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: 17.5°
Explanation:
Correct Answer: BC > CA, CA < CD
Explanation:
According to question,
?B = ?C = 55° , ?D = 25°
We can say ,
AB = AC ( ? ?B = ?C = 55° )
In Triangle ABC,
?A + ?B + ?C = 180°
? ?A + 55° + 55° = 180°
? ?A + 110° = 180°
? ?A = 180° - 110°
? ?A = 70° ..........................(1)
As per given figure,
?ACD + ?ACB = 180° ( ?ACB = ?C = 55°)
? ?ACD + 55° = 180°
? ?ACD = 180° - 55°
? ?ACD = 125° ....................... (2)
Now in Triangle ACD,
?CAD + ?ACD + ?CDA = 180°
? ?CAD + 125° + 25° = 180°
? ?CAD + 150° = 180°
? ?CAD = 30° ...........................(3)
( In a ?, greater angle has longer side opposite to it )
From the equation (1) , (2) and (3);
?B < ?A and ?CAD > ?D ;
? BC > CA and CA < CD
Correct Answer: Rectangle
Explanation:
Correct Answer: 90°
Explanation:
Since OP bisects ?BOC,
? ?BOC = 2?POC
Again, OQ bisects ?AOC,
? ?AOC = 2?QOC
Since ray OC stands on line AB, ?,
?AOC + ?BOC = 180°
? 2?QOC + 2?POC = 180°
? 2?QOC + ?POC = 180°
? ?QOC + ?POC = 90°
? ?POQ = 90°.
The above sum can also be restated as follows; The angle between the bisectors of a linear pair of angles is a right angle.
Correct Answer: 1 4
Explanation:
Correct Answer: 60 m
Explanation:
Correct Answer: AD2 = BD × CD
Explanation:
Correct Answer: AB2 + BC2+ CD2 + DA2 = AC2 + BD2
Explanation:
In ||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 }
Correct Answer: 9 16
Explanation:
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