Question

On a piece of paper, use a protractor and a ruler to construct △ABC with AB=5 in. , AC=5 in. , and ​ m∠A=60° ​ . Which statement is true about this triangle? BC=3 in. BC=4 in. BC=5 in. The length of BC¯¯¯¯¯ cannot be measured.

Answer 1

Answer: B) BC=4 in.

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: BC=5 in. is the correct answer.

Step-by-step explanation: