Geometric Analysis: Determining Acute Triangle Properties

Question

Is the triangle in the drawing an acute-angled triangle?

Video Solution

Solution Steps

00:00 Determine whether the triangle is acute
00:04 Draw the perpendicular to our angle
00:14 We observe that our angle is larger than a right angle
00:31 Apply the same method to another angle
00:40 We observe that it's smaller than the right angle
00:47 A triangle with an angle greater than 90° is an obtuse triangle
00:51 This is the solution

Step-by-Step Solution

To determine if the triangle is an acute-angled triangle, we need to understand the nature of its angles. In an acute-angled triangle, all three angles are less than 9090^\circ. However, we do not have explicit angle measures or side lengths shown in the drawing. Instead, we assess the probable nature of the depicted triangle.

Given that an acute-angled triangle must have its largest angle smaller than 9090^\circ, comparison property of triangle sides through Pythagorean type logic suggests that an acute triangle inequality c2<a2+b2c^2 < a^2 + b^2 (for sides aa, bb, and hypotenuse cc) must hold.

In our problem, the depiction ultimately leads us to infer the implied relations among the triangle's angles. The given solution and analysis indicate it does not meet this criterion.

Hence, the triangle in the given drawing is not an acute-angled triangle, confirming the choice: No.

Answer

No