Question

In ΔEFG, m∠E=30°, m∠F=60°, and m∠G=90°. Which of the following statements about ΔEFG are true? Check all that apply.

a) ΔEFG is a right-angled triangle.

b) ΔEFG is an equilateral triangle.

c) The sum of the angles in ΔEFG is 180°.

d) EF is the hypotenuse of ΔEFG.

Answer 1

∆EFG is indeed a right-angled triangle with a sum of angles of 180°, and EF is its hypotenuse, but it is not an equilateral triangle.

Step-by-step explanation:

The properties of ∆EFG given the angles m∠E=30°, m∠F=60°, and m∠G=90°, can be deduced.

• a) ∆EFG is a right-angled triangle: This is true because one of the angles is 90°, which is the defining characteristic of a right-angled triangle.
• b) ∆EFG is an equilateral triangle: This statement is false because an equilateral triangle has all three angles equal, which is not the case here.
• c) The sum of the angles in ∆EFG is 180°: This is true, as it is a basic property of all triangles that their angles sum up to 180 degrees.
• d) EF is the hypotenuse of ∆EFG: This is true, assuming ∠G is opposite EF, as EF would be opposite the right angle, making it the longest side and hence the hypotenuse.