Question

A triangle with two acute angles must be a right triangle. True or False

Answer 1

False. Because two acute angles just make an acute angle. Its like saying 1x1=1. make sense? 

Answer 2

False

Explanation:

We are given that a triangle in which two acute angles .

Then, the triangle must be a right triangle .

We have to find that it is true or false.

Acute angle: That angle whose measure is less than 90 degrees.

Right triangle : That triangle in which one angle measure is equal to 90 degrees.

Let x, y and z are angles of a triangle

Suppose, we have x=70 degrees , y= 60 degrees

Then ,
`x+y+z=180^(\circ)` (triangle angles sum property)

`70+60+z=180`

`130+z=180`

`z=180-130=50^(\circ)\\eq 90^(\circ)`

Hence, the triangle must not be right triangle in that case.

When x=y=45 degrees

Then ,
`45+45+z=180`

`90+z=180`

`z=180-90=90^(\circ)`

Hence, the triangle must be right triangle in that case.

Therefore, a triangle with acute angles must be right triangle is true when two acute angles measure are of 45 degrees each not in every case.

Hence, a triangle with two acute angles must not be a right triangle.

Answer: False