Discussion
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- Question
- If one of the diagonals of a rhombus is equal to its side, then the diagonals of the rhombus are in the ratio :
Options- A. ?3 : 1
- B. ?2 : 1
- C. 3 : 1
- D. 2 : 1
- Correct Answer
- ?2 : 1
ExplanationLet ABCD is a rhombus in which AB = BC = CD = DA = diagonal CA.
In triangle ABC ,
AB = BC = CA , therefore ?B = 60°
?D = ?B = 60°
?A=180 - ?B = 180° - 60° =120°
?C = ?A=120°
Hence ,The ratio of diagonals = ?2 : 1 - 1. The two sides of a right triangle containing the right angle measure 3 cm and 4 cm. The radius of the in circle of the triangle is :
Options- A. 3.5 cm
- B. 1.75 cm
- C. 1 cm
- D. 0.875 cm Discuss
- 2. PQRS is a square. The ? SRP is equal to :
Options- A. 45°
- B. 90°
- C. 100°
- D. 60° Discuss
- 3. In fig, AB = AC, D is a point on AC and E on AB such that AD = ED = EC = BC. Then ?A : ?B :
Options- A. 1 : 2
- B. 2 : 1
- C. 3 : 1
- D. 1 : 3 Discuss
- 4. In the given figure, side BC of ? ABC is produced to form ray BD and CE || BA. Then ? ACD is equal to :
Options- A. ?A - ?B
- B. 1 (?A + ?B) 2
- C. ?A + ?B
- D. 1 (?A - ?B) 2 Discuss
- 5. If the sides of a triangle are produced then the sum of the exterior angles i.e., ? a + ? b + ? c is equal to :
Options- A. 180°
- B. 90°
- C. 360°
- D. 270° Discuss
- 6. We have an angle of 2 1°/ 2 .How big it will look through a glass that magnifies things three times?
Options- A. 2 1° × 4 2
- B. 2 1° × 3 2
- C. 2 1° × 2 2
- D. 2 1° × 5 2 Discuss
- 7. Two circles of unit radius touch each other and each of them touches internally a circle of radius two, as shown in the following figure. The radius of the circle which thouches all the three circles:
Options- A. 5
- B. 3 2
- C. 2 3
- D. 2 5 Discuss
- 8. If, in the following figure, PA = 8 cm, PD = 4 cm, CD equal to 3 cm, then AB is :
Options- A. 3.0 cm
- B. 3.5 cm
- C. 4.0 cm
- D. 4.5 cm Discuss
- 9. In the given figure, what is the length of AD in terms of b and c :
Options- A. bc b2+c2
- B. b2+c2 bc
- C. ? b2+c2 bc
- D. bc ? b2+c2 Discuss
- 10. In a quadrilateral ABCD, ?B = 90° and AD 2 = AB 2 + BC 2 + CD 2, then ?ACD is equal to:
Options- A. 90°
- B. 60°
- C. 30°
- D. 20° Discuss
Plane Geometry problems
Search Results
Correct Answer: 1 cm
Explanation:
Correct Answer: 45°
Explanation:
Correct Answer: 1 : 3
Explanation:
Correct Answer: ?A + ?B
Explanation:
From above given figure , we can see that
CE || BA and AC is the transversal.
? ?4 = ?1 (alternate interior ?s) .......... ( 1 )
Again, CE || BA and BD is the transversal.
? ?5 = ?2 (corresponding ?s) ................( 2 )
Adding equations ( 1 ) and ( 2 )
? ?4 + ?5 = ?1 + ?2
??ACD = ?A + ?B.
Correct Answer: 360°
Explanation:
From above figure , we have
Since every exterior angle is equal to sum of interior opposite angles,
So, ? a = A + B, ? b = B + C and ? c = A + C
We know that , A + B + C = 180°
? ?a +?b + ?c = 2(A + B + C) = 2 × 180° = 360°.
Correct Answer: 2 1° × 5 2
Explanation:
Correct Answer: 2 3
Explanation:
Correct Answer: 4.5 cm
Explanation:
Correct Answer: bc ? b2+c2
Explanation:
Correct Answer: 90°
Explanation:
In a quadrilateral ABCD,
Given :- ?B = 90°
AB2 + BC2 + CD2 = AC2 + CD2 = AD2 { ? In triangle ABC , AB2 + BC2 = AC2 }
So, in triangle ACD, angle opposite to AD = 90° ( by Converse of Pythagoras theorem)
? ?ACD = 90°
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