Question

It is impossible for a triangle to be which of the following?

a. both equilateral and acute
b. both right and acute
c. both isosceles and acute
d. both scalene and acute

Answer 1

Think about the definitions, what it takes to be equilateral, right, isosceles, and scalene; and what it takes to be acute.

Only one of the first 4 is contradictory with the definition of an acute triangle.

Answer 2

This may help:
http://www.mathsisfun.com/triangle.html

Answer 3

a. Scalene and isosceles - NO
Scalene means that all three sides have unequal lengths.
Isosceles means that at least two sides are equal.

b. Isosceles and equilateral - YES
All equilateral triangles are isosceles, but not all isosceles triangles are equilateral.

c. Scalene and equilateral - NO (see explanation for (a) and (b))

d. Right and acute angled - NO (acute-angled means that ALL 3 angles are less than 90 degrees).

e. Right and acute angled - NO (obtuse angled means that 1 angle is greater than 90 degrees). 2*90 = 180. If one angle is 90 degrees, the other 2 angles MUST be less than 90 degrees (their sum must be 90 degrees and negative angles are not permitted.)

f. Acute angled and obtuse angled - NO. Obtuse angled means that 1 angle is greater than 90 degrees. Acute-angled means that ALL 3 angles are less than 90 degrees.

Answer 4

That help?

Answer 5

That's not the question. I'm asking which two properties a triangle can't have.

Answer 6

@DebbieG So would it be Right and Acute?

Answer 7

If you think about an equilateral triangle, you know that it is also equiangular and, since the sum of the three angles in any triangle is 180 degrees, the angles in an equilateral triangle must be 60 degrees each. So, each angle is an acute angle (A < 90) so answer D) cannot be true.

Answer 8

OK?

Answer 9

Yes, it is right and acute. Acute cannot have any angle 90* or greater, and right must have a 90* angle. :)

Answer 10

Well, it couldn't be right and acute could it? Because right means 90 degrees, and acute means less than 90 degrees

Answer 11

Oh, thanks Debbie, I didn't see your response :)

Answer 12

You're welcome. :)