Which of the statements is ALWAYS TRUE?

A-A right triangle is a scalene triangle.
B-An equilateral triangle is an isosceles triangle.
C-An isosceles triangle is an obtuse triangle.
D-A right triangle is an acute triangle.
I got either A or D. I don't know.

Also, if angle A is 26.5, angle B is 3 times angle A, would angle C be 74, and would the triangle be a scalene?

B

angle C = 74 , yes

Thanks so much!! :D

Answer is B

Very cool

Wow UwU

To determine which of the statements is always true, we can analyze each statement individually:

Statement A: A right triangle is a scalene triangle.
A right triangle is a triangle that contains a right angle (90 degrees). A scalene triangle is a triangle with all three sides of different lengths.

Explanation: A right triangle can have sides of different lengths, making it possible for it to be a scalene triangle. However, a right triangle can also have two sides of equal length, making it an isosceles triangle. Therefore, statement A is not always true.

Statement B: An equilateral triangle is an isosceles triangle.
An equilateral triangle is a triangle with all three sides of equal length. An isosceles triangle is a triangle with at least two sides of equal length.

Explanation: An equilateral triangle has all three sides of equal length, which means it also has at least two sides of equal length. Therefore, statement B is always true.

Statement C: An isosceles triangle is an obtuse triangle.
An isosceles triangle is a triangle with at least two sides of equal length. An obtuse triangle is a triangle with one angle greater than 90 degrees.

Explanation: An isosceles triangle can have any angle measures, including acute (all angles less than 90 degrees) or right (one angle of 90 degrees). Therefore, an isosceles triangle is not always obtuse. Consequently, statement C is not always true.

Statement D: A right triangle is an acute triangle.
An acute triangle is a triangle with all three angles less than 90 degrees. A right triangle is a triangle with one right angle (90 degrees).

Explanation: A right triangle by definition has one right angle, which means it cannot have all three angles less than 90 degrees, as required for an acute triangle. Therefore, statement D is not always true.

Considering the analysis, the correct option is B: An equilateral triangle is an isosceles triangle, which is always true.

Regarding the given angles (angle A = 26.5 degrees and angle B = 3 times angle A), let's find angle C and determine if the triangle is scalene:

Given: Angle A = 26.5 degrees
Angle B = 3 * Angle A (3 times Angle A)

To find Angle B, multiply Angle A by 3:
Angle B = 3 * 26.5 degrees = 79.5 degrees

To find Angle C, subtract the sum of Angle A and Angle B from 180 degrees (the sum of angles in a triangle):
Angle C = 180 degrees - (Angle A + Angle B)
Angle C = 180 degrees - (26.5 degrees + 79.5 degrees)
Angle C = 180 degrees - 106 degrees
Angle C = 74 degrees

Therefore, Angle C is 74 degrees.

To determine if the triangle is scalene, we need to compare the lengths of its sides. However, the information provided in the question does not contain any details about the side lengths. Thus, we cannot conclude whether the triangle is scalene based on the given information.