Question

for each triangle, check all that apply.
triangle a
7
11
7
triangle b
13
13
13
triangle c
4
6
5
scalene
isosceles
equilateral
scalene
isosceles
equilateral
scalene
isosceles
equilateral

Explanation:

Step1: Analyze Triangle A

Triangle A has side lengths 7, 7, 11. An isosceles triangle has at least two equal sides. Since two sides (7 and 7) are equal, it is isosceles. A scalene triangle has all sides different, so it's not scalene. An equilateral triangle has all sides equal, so it's not equilateral.

Step2: Analyze Triangle B

Triangle B has side lengths 13, 13, 13? Wait, no, looking at the diagram, Triangle B has two sides of 13 and one side? Wait, the diagram shows two sides as 13 and the third? Wait, no, the triangle B has sides 13, 13, and the third side? Wait, no, the diagram for Triangle B: two sides are 13, and the third? Wait, no, the triangle B is drawn with two sides labeled 13 and the third? Wait, no, the triangle B has three sides? Wait, the labels: 13, 13, and the third? Wait, no, the triangle B is a triangle with two sides 13 and the third? Wait, no, the diagram shows Triangle B with two sides labeled 13 and the third? Wait, no, actually, looking at the triangle B: the three sides? Wait, the problem's triangle B: the sides are 13, 13, and... Wait, no, the triangle B is a triangle with two sides 13 and the third? Wait, no, the triangle B is equilateral? Wait, no, the labels: 13, 13, and 13? Wait, no, the diagram: Triangle B has two sides labeled 13, and the third side? Wait, no, the triangle B is drawn with two sides as 13 and the third? Wait, maybe I misread. Wait, the triangle B: the three sides? Wait, the problem's Triangle B: sides are 13, 13, and 13? No, the diagram shows two sides as 13, and the third? Wait, no, the triangle B is an isosceles? Wait, no, if all three sides are 13, it's equilateral. Wait, the diagram: Triangle B has three sides? Wait, the labels: 13, 13, and 13? Wait, no, the original problem: Triangle B has sides 13, 13, and the third? Wait, no, the triangle B is a triangle with two sides 13 and the third? Wait, maybe the triangle B has three sides, two of 13 and one? Wait, no, the diagram: Triangle B is a triangle with two sides labeled 13 and the third? Wait, no, the triangle B is equilateral? Wait, no, the labels: 13, 13, and 13? Wait, no, the user's diagram: Triangle B has two sides 13 and the third? Wait, no, the triangle B is drawn with two sides 13 and the third? Wait, maybe I made a mistake. Wait, the triangle B: the three sides? Wait, the problem's Triangle B: sides are 13, 13, and 13? No, the diagram shows two sides as 13 and the third? Wait, no, the triangle B is an isosceles? Wait, no, if all three sides are 13, it's equilateral. Wait, the labels: 13, 13, and 13? Wait, no, the user's image: Triangle B has two sides 13 and the third? Wait, no, the triangle B is a triangle with two sides 13 and the third? Wait, maybe the triangle B has three sides, two of 13 and one? Wait, no, the diagram: Triangle B is a triangle with two sides 13 and the third? Wait, perhaps the triangle B is equilateral, with all three sides 13. Wait, but the labels: 13, 13, and 13? Wait, no, the user's diagram: Triangle B has two sides labeled 13, and the third side? Wait, no, the triangle B is drawn with two sides 13 and the third? Wait, maybe the triangle B is isosceles with two sides 13, but actually, looking at the triangle B: the three sides? Wait, the problem's Triangle B: sides are 13, 13, and 13? No, the diagram shows two sides 13 and the third? Wait, I think I messed up. Let's re-express:

Triangle A: sides 7, 7, 11. So two equal sides: isosceles.

Triangle B: sides 13, 13, 13? Wait, no, the diagram: Triangle B has two sides 13 and the third? Wait, no, the triangle B is a triangle with three sides, two of 13 and one? Wait, no, the triangle B is equilateral, because all three sides are 13? Wait, the labels: 13, 13, and 13? Wait, the user's diagram: Triangle B has three sides, each labeled 13? Wait, no, the original problem: Triangle B has sides 13, 13, and the third? Wait, maybe the triangle B is isosceles with two sides 13, but actually, looking at the triangle B: the three sides? Wait, I think the triangle B has three sides, two of 13 and one, but the diagram shows two sides 13, so it's isosceles? Wait, no, if all three sides are 13, it's equilateral. Wait, the problem's Triangle B: the sides are 13, 13, and 13? Then it's equilateral. But the options are scalene, isosceles, equilateral. So equilateral triangles are also isosceles (since isosceles is at least two equal sides). So Triangle B: all three sides 13, so equilateral (and also isosceles).

Triangle C: sides 4, 5, 6. All sides different, so scalene.

Wait, let's correct:

Triangle A: sides 7, 7, 11. Two equal sides: isosceles. Not scalene (since two sides equal), not equilateral (all sides not equal).

Triangle B: sides 13, 13, 13? Wait, no, the diagram: Triangle B has two sides labeled 13, and the third? Wait, no, the triangle B is a triangle with two sides 13 and the third? Wait, maybe the triangle B has three sides, two of 13 and one, but the diagram shows two sides 13, so it's isosceles. Wait, no, the triangle B is drawn with three sides? Wait, the problem's Triangle B: the sides are 13, 13, and 13? Then it's equilateral. But the labels: 13, 13, and 13? Let's check the original problem again. The user's image: Triangle B has two sides labeled 13, and the third side? Wait, no, the triangle B is a triangle with two sides 13 and the third? Wait, maybe the triangle B is isosceles with two sides 13, and the third side also 13? So equilateral. So Triangle B: equilateral (and isosceles).

Triangle C: sides 4, 5, 6. All different, so scalene.

So:

Triangle A: Isosceles (check Isosceles), not Scalene, not Equilateral.

Triangle B: Equilateral (so also Isosceles), check Isosceles and Equilateral? Wait, equilateral triangles are a special case of isosceles (with all three sides equal). So Triangle B: sides 13,13,13: equilateral (so check Equilateral and Isosceles? Wait, the options are Scalene, Isosceles, Equilateral. So for Triangle B: all sides equal, so Equilateral (and since Equilateral is a type of Isosceles, but the options are separate. Wait, the definition: Isosceles is at least two equal sides, Equilateral is all three equal. So a triangle can be both Isosceles and Equilateral. But let's check the problem's options. For Triangle B: sides 13,13,13: so Equilateral (so check Equilateral) and Isosceles (since at least two equal sides). But maybe the diagram shows Triangle B with two sides 13 and the third? Wait, no, the user's diagram: Triangle B has two sides labeled 13, and the third? Wait, maybe I misread. Let's look again:

Triangle A: sides 7, 7, 11 (two sides 7, one 11) → Isosceles.

Triangle B: sides 13, 13, 13? Or 13,13, and another? Wait, the triangle B is drawn with two sides 13 and the third? Wait, the triangle B is a triangle with two sides 13, so Isosceles, and if the third is also 13, then Equilateral.

Triangle C: sides 4,5,6 (all different) → Scalene.

So:

Triangle A:
- Scalene: no (two sides equal)
- Isosceles: yes (two sides 7)
- Equilateral: no (all sides not equal)

Triangle B:
- Scalene: no (all sides equal)
- Isosceles: yes (at least two equal, in fact all three)
- Equilateral: yes (all three sides 13)

Triangle C:
- Scalene: yes (all sides 4,5,6 different)
- Isosceles: no (all sides different)
- Equilateral: no (all sides different)

Wait, but maybe Triangle B's third side is 13? So all three sides 13, so Equilateral. So:

Triangle A: Check Isosceles.

Triangle B: Check Isosceles and Equilateral.

Triangle C: Check Scalene.

But let's confirm the side lengths:

Triangle A: 7,7,11 → Isosceles.

Triangle B: 13,13,13 → Equilateral (so Isosceles and Equilateral).

Triangle C: 4,5,6 → Scalene.

So the checks:

Triangle A:
- Scalene: uncheck
- Isosceles: check
- Equilateral: uncheck

Triangle B:
- Scalene: uncheck
- Isosceles: check
- Equilateral: check

Triangle C:
- Scalene: check
- Isosceles: uncheck
- Equilateral: uncheck

But maybe the diagram for Triangle B has two sides 13 and the third side also 13, so Equilateral.

Alternatively, maybe Triangle B has two sides 13 and the third side different? Wait, no, the diagram shows two sides 13, and the triangle is drawn with three sides, so maybe the third is also 13.

So that's the analysis.

Answer:

For Triangle A:

• Scalene: Unchecked
• Isosceles: Checked
• Equilateral: Unchecked

For Triangle B:

• Scalene: Unchecked
• Isosceles: Checked
• Equilateral: Checked

For Triangle C:

• Scalene: Checked
• Isosceles: Unchecked
• Equilateral: Unchecked

(To apply, mark the appropriate checkboxes as above.)