Question

On a piece of paper, use a protractor and a ruler to construct △ABC with AB=4 in. , AC=4 in. , and m∠A=60° . Which statement is true about this triangle?
A) BC=3 in.
B) BC=4 in.
C) BC=5 in.
D) BC can not be measured

Answer 1

Answer: B) BC=4 in.

Step-by-step explanation:

Given: In △ABC , AB=4 inch ,AC=4 in. , and m∠A=60°

⇒ AB=AC= 4 inches

⇒ △ABC is an isosceles triangle.

⇒ m∠A=60°=m∠B   [angles opposite to the equal sides of a triangle are equal]

Now by angle sum property,

m∠A+m∠B+m∠C=180°

⇒60°+60°+m∠C=180°

⇒ m∠C=180°-120°

⇒ m∠C=60°

⇒ △ABC is an equilateral triangle.

⇒ BC= 4 inches [sides of an equilateral triangles are equal]

⇒ B is the right answer.

Answer 2

Answer: B) BC=4 in.

Step-by-step explanation:

Given: In △ABC , AB=4 inch ,AC=4 in. , and m∠A=60°

⇒ AB=AC= 4 inches

⇒ △ABC is an isosceles triangle.

⇒ m∠A=60°=m∠B   [angles opposite to the equal sides of a triangle are equal]

Now by angle sum property,

m∠A+m∠B+m∠C=180°

⇒60°+60°+m∠C=180°

⇒ m∠C=180°-120°

⇒ m∠C=60°

⇒ △ABC is an equilateral triangle.

⇒ BC= 4 inches [sides of an equilateral triangles are equal]

⇒ B is the right answer.