Plane Geometry
- If in a triangle ABC as drawn in the figure, AB = AC and ∠ ACD = 120°, then ∠ A is equal to A
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On the basis of given question , we draw a figure of triangle ABC
Given , AB = AC and ∠ ACD = 120°
∠ ACB = 180° - ∠ ACD = 180° – 120° = 60°Correct Option: B
On the basis of given question , we draw a figure of triangle ABC
Given , AB = AC and ∠ ACD = 120°
∠ ACB = 180° - ∠ ACD = 180° – 120° = 60°
∴ ∠ ABC = ∠ ACB = 60°
∴ ∠ BAC = 60°
- Let ABC be an equilateral triangle and AD perpendicular to BC. Then AB² + BC² + CA² = ?
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As per the given in question, we draw a figure of an equilateral triangle ABC
Here , AD ⊥ BC
∴ BD = DC = AB/2 = AC/2 = CB/2
Use the Pythagoras formula to get the length of AD.AD = √3 AB = √3 BC = √3 AC 2 2 2 Correct Option: D
As per the given in question, we draw a figure of an equilateral triangle ABC
Here , AD ⊥ BC
∴ BD = DC = AB/2 = AC/2 = CB/2
Use the Pythagoras formula to get the length of AD.AD = √3 AB = √3 BC = √3 AC 2 2 2 ⇒ AB = 2 AD = BC = AC √3 ∴ AB² + BC² + AC² = 
4 + 4 + 4 
AD² = 4AD² 3 3 3
- The centroid of an equilateral triangle ABC is G and AB = 10 cm. The length of AG (in cm) is :
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We draw a figure of an equilateral triangle ABC whose G is centroid and AB = 10 cm
BD = DC = 5 cm
∠ADB = 90°
∴ AB² = BD² + AD²
⇒ 10² = 5² + AD²
⇒ 100 = 25 + AD²
⇒ AD² = 100 - 25 = 75
∴ AD = √75 = 5√3Correct Option: C
We draw a figure of an equilateral triangle ABC whose G is centroid and AB = 10 cm
BD = DC = 5 cm
∠ADB = 90°
∴ AB² = BD² + AD²
⇒ 10² = 5² + AD²
⇒ 100 = 25 + AD²
⇒ AD² = 100 - 25 = 75
∴ AD = √75 = 5√3∴ AG = 2 AD = 2 × 5√3 = 10√3 cm. 3 3 3
- The altitude of an equilateral triangle of side 2/√3 cm is :
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We draw a figure of an equilateral triangle ABC ,
Given , AB = 2 cm. √3 BD = BC 2 BD = 2 = 1 cm. 2√3 √3
∴ AD = √AB² - BD²
Correct Option: D
We draw a figure of an equilateral triangle ABC ,
Given , AB = 2 cm. √3 BD = BC 2 BD = 2 = 1 cm. 2√3 √3
∴ AD = √AB² - BD²AD = √ 4 - 1 3 3 AD = √ 3 = 1 cm. 3
- The centroid of an equilateral triangle ABC is G. If AB is 6 cms, the length of AG is
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We draw a figure of an equilateral triangle ABC whose G is centroid and side is 6 cm ,
AB = 6 cm.; AD ⊥ BC
∴ BD = DC = 3 cm.
In ∆ABD,
AD = √AB² – BD²
AD = √6² – 3²
AD = √36 - 9
AD = √27 = 3 √3 cm.Correct Option: B
We draw a figure of an equilateral triangle ABC whose G is centroid and side is 6 cm ,
AB = 6 cm.; AD ⊥ BC
∴ BD = DC = 3 cm.
In ∆ABD,
AD = √AB² – BD²
AD = √6² – 3²
AD = √36 - 9
AD = √27 = 3 √3 cm.∴ AG = 2 AD = 2 × 3√3 3 3
AG = 2√3 cm.
