Classify the triangle by its angles and sides.
obtuse isosceles
equiangular equilateral
acute isosceles
acute scalene
2 of 10
I think I'd rather classify the poster as obtuse and obfuscatory
1. A. 79°
2. triangle QPR congruent to triangle STR; ASA
3. B. angleCBX and angleFBC
4. C. 52º
5. A. 115°
6. D. scalene acute
7. C. No; corresponding angles are not congruent.
8. D. alternate interior
9. C. 1,260°
10. B. 150°
Well, it seems like you've got a little bit of everything here - a triangle smorgasbord, if you will. Let's break it down, shall we?
First up, we have the "obtuse isosceles." Now, this triangle's angles are anything but acute - in fact, one of them is obtuse. And to add a little spice to the mix, it's also isosceles, meaning two of its sides are equal in length. So you've got a triangle that's a bit lopsided but still manages to find some symmetry.
Next, we have the "equiangular equilateral" triangle. This one is all about equality - it's got three angles that are all equal, making it equiangular. And just to keep things fair, all three of its sides are also equal in length, which earns it the title of equilateral. So this triangle is all about sharing the love and keeping everything nice and balanced.
Then we have the "acute isosceles." Now, this triangle is all about being acute - none of its angles are obtuse or right angles, they're all less than 90 degrees. And just like our first triangle, it's also isosceles, meaning two of its sides are equal. So you've got a triangle that's both sharp and symmetrical.
Lastly, we have the "acute scalene." This triangle is all about being acute, just like the previous one - all of its angles are smaller than 90 degrees. But unlike the others, it's also scalene - meaning all of its sides are different lengths. So this triangle is all about being unique and not conforming to any rules.
So there you have it - obtuse isosceles, equiangular equilateral, acute isosceles, and acute scalene. It's a triangle buffet with a side of humor. Enjoy!
To classify a triangle by its angles and sides, we need to understand the definitions of different types of triangles:
1. Equiangular Triangle: This is a triangle where all three angles are equal. Since the sum of angles in any triangle is always 180 degrees, in an equiangular triangle, each angle must measure 60 degrees. An equiangular triangle is also equilateral.
2. Equilateral Triangle: This is a triangle where all three sides are equal in length. Equilateral triangles are also equiangular because all three angles are 60 degrees.
3. Isosceles Triangle: This is a triangle that has at least two sides of equal length. The angles opposite the equal sides are also equal.
4. Scalene Triangle: In a scalene triangle, all three sides are of different lengths. Similarly, the angles within a scalene triangle are also different.
Now, let's classify each of the given triangles:
1. Obtuse Isosceles Triangle: An obtuse triangle is one that has one angle greater than 90 degrees. So, an obtuse isosceles triangle would have a least two equal sides, and one angle larger than 90 degrees.
2. Equiangular Equilateral Triangle: As mentioned earlier, an equiangular triangle is always equilateral. So, an equiangular equilateral triangle is one where all three angles and all three sides are equal.
3. Acute Isosceles Triangle: An acute triangle is one where all three angles are less than 90 degrees. An acute isosceles triangle has two equal sides and all three angles less than 90 degrees.
4. Acute Scalene Triangle: An acute scalene triangle is simply a triangle where all three angles are less than 90 degrees, and all three sides have different lengths.
From the given options, the triangles that match these classifications are:
- Obtuse Isosceles
- Equiangular Equilateral
- Acute Isosceles
- Acute Scalene
Therefore, two out of the ten options belong to these classifications.