Plane Geometry
- Astha cuts a triangle out of a cardboard and tries to balance the triangle horizontally at the tip of her finger. On what point will she be able to balance the shape for any kind of triangle?
-
View Hint View Answer Discuss in Forum
As per the given question ,
Astha cuts a triangle out of a cardboard and tries to balance the triangle horizontally at the tip of her finger.Correct Option: C
As per the given question ,
Astha cuts a triangle out of a cardboard and tries to balance the triangle horizontally at the tip of her finger. The centroid is the centre of gravity.
- BE and CF are two altitudes of a triangle ABC. If AB = 6 cm, AC = 5 cm and CF = 4 cm, then the length of BE is
-
View Hint View Answer Discuss in Forum
As per the given in question , we draw a figure triangle ABC in which BE and CF are two altitudes ,
Here , AB = 6 cm, AC = 5 cm and CF = 4 cmArea of ∆ ABC = 1 × AB × CF 2 Area of ∆ ABC = 1 × 6 × 4 = 12Sq. cm. 2
Again,area of ∆ ABC = 1 × AC × BE 2 ⇒ 12 = 1 × 5 × BE 2
Correct Option: A
As per the given in question , we draw a figure triangle ABC in which BE and CF are two altitudes ,
Here , AB = 6 cm, AC = 5 cm and CF = 4 cmArea of ∆ ABC = 1 × AB × CF 2 Area of ∆ ABC = 1 × 6 × 4 = 12Sq. cm. 2
Again,area of ∆ ABC = 1 × AC × BE 2 ⇒ 12 = 1 × 5 × BE 2
⇒ 5 × BE = 2 × 12 = 24⇒ BE = 24 = 4.8 cm. 5
- In a ∆ABC, BC is extended upto D. ∠ACD = 120°, ∠B = 1/2 ∠A. Then ∠A is
-
View Hint View Answer Discuss in Forum
We draw a figure triangle ABC whose BC is extended upto D point ,
Exterior ∠ACD = Interior (∠BAC + ∠ABC)⇒ 120° = ∠A + ∠A 2
⇒ 240 = 2∠A + ∠A
⇒ 3∠A = 240°
Correct Option: C
We draw a figure triangle ABC whose BC is extended upto D point ,
Exterior ∠ACD = Interior (∠BAC + ∠ABC)⇒ 120° = ∠A + ∠A 2
⇒ 240 = 2∠A + ∠A
⇒ 3∠A = 240°⇒ ∠A = 240° = 80° 3
- In ∆ ABC, D is the mid–point of BC and G is the centroid. If GD = 5 cm, then the length of AD is :
-
View Hint View Answer Discuss in Forum
As per the given in question , we draw a figure triangle ABC in which D is the mid–point of BC and G is the centroid ,
We know that , AG : GD = 2 : 1Correct Option: C
As per the given in question , we draw a figure triangle ABC in which D is the mid–point of BC and G is the centroid ,
We know that , AG : GD = 2 : 1
AD = 3GD = 3 × 5 = 15 cm.
- Possible measures of three angles of a triangle are
-
View Hint View Answer Discuss in Forum
As we know that The sum of all the angles of a triangle is 180°.
From option (4) ,
50° + 60° + 70° = 180°Correct Option: D
As we know that The sum of all the angles of a triangle is 180°.
From option (4) ,
50° + 60° + 70° = 180°
Hence , Possible measures of three angles of a triangle are 50°, 60° and 70° .
