Classify the triangle below according to its sides and angles. I. Equilateral II. Isosceles III. Scalene IV. Acute V. Obtuse VI. Right

Everyone. Welcome back. So in this practice problem here, we're gonna classify this triangle according to its sides and also its angles. Let's go ahead and get started here. Now remember that there's 3 ways to classify a triangle based on its sides. Those are equilateral, isosceles, and scaling. All of these have to do with of the side lengths of a triangle. Remember that equilateral means that all the the three sides of the triangle have to be the same, and we indicate that by using these little tick marks over here. I see 2 tick marks, but not 3. That means that this side over here, the longest side, is different than the other 2. So it's definitely not an equilateral triangle. A scalene triangle would mean that all of the sides would be different, so meaning none of the sides would be the same. So it's not a scalene triangle, so this is an isosceles triangle. This means that 2 of the sides are the same, and that's exactly what we see over here. We see these 2 tick marks. So it's an isosceles triangle. What about the angles? Well, remember that there's 3 other categories or types of triangles that we have based on the relationship of the angles in a triangle. So remember that we have acute, obtuse, and right, and this just has to do with the angle measurements. Acute means that all of the angles have to be less than 90 degrees. Obtuse means that at least one of the angles needs to be more than 90, and a right triangle means that one of the angles is exactly 90 degrees. So in order to figure this out, notice that we only have 2 of the angle measurements, 30 and 30, so we actually have to figure out what the unknown angle is first before we can classify it. We can actually do that really quickly here because remember that all of the angles have to add up to a 180 degrees in a triangle. So we can set up a little equation over here. It's pretty straightforward. 30 plus 30 plus some unknown angle, which is theta over here, is gonna equal a 180 degrees. Alright? So how do we solve for this? We're just gonna knock 30 off of both sides, minus 30, and this is the same thing as subtracting 60 from both sides. So what we're gonna see here is that theta is equal to a 180 minus 60, which is a 120 degrees. So now we know what this unknown angle is. It's a 120. Now that we know this, we can figure out where we can sort of classify it. Right? So it's definitely not an acute triangle because we have one angle that's larger than 90, so all of them are not less than 90. So that also means that it's not a right triangle either because there isn't one that's exactly 90. Instead, it's an obtuse triangle. So we're dealing with an isosceles obtuse triangle, and that's how we would classify this triangle over here. So that means that in terms of the, selections we have over here, it's 2 and 5, and that would be the correct answer. Alright. So these are the 2 classifications. Let me know if you have any questions, and let's move on.

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Classify the triangle below according to its sides and angles.I. EquilateralII. IsoscelesIII. ScaleneIV. AcuteV. ObtuseVI. Right

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Classify the triangle below according to its sides and angles.
$Isosceles triangle with two equal sides and two 30-degree angles at the base, labeled with angle theta at the top.$
I. Equilateral
II. Isosceles
III. Scalene
IV. Acute
V. Obtuse
VI. Right