Identify the type of each triangle based on side lengths and angles.

Let's solve the problem step by step.

We are asked to identify the type of each triangle based on its angles and side lengths. Triangles can be classified in two main ways:

1. By Angles:

- Acute: All three angles are less than 90°.
- Right: One angle is exactly 90° (marked with a square).
- Obtuse: One angle is greater than 90°.

2. By Sides:

- Scalene: All sides have different lengths.
- Isosceles: Two sides are equal.
- Equilateral: All three sides are equal.

Now, let’s analyze each triangle one by one.

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1)

- Has a right angle (square symbol at corner).
- Sides: a, b, c (with c being the hypotenuse).
- Type: Right triangle (by angle), and since all sides are labeled differently (a, b, c), likely scalene.
- ✔ Answer: Right Scalene

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2)

- No right angle shown.
- Sides: a, b, c — all different labels → all sides different.
- Looks like it has one angle larger than others → possibly obtuse.
- But no markings — just based on shape: appears to have one large angle.
- Since no right angle, and sides unequal → Obtuse Scalene
- ✔ Answer: Obtuse Scalene

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3)

- No right angle.
- Sides: a, b, c — all different → scalene.
- Appears to have one angle greater than 90° → obtuse.
- ✔ Answer: Obtuse Scalene

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4)

- Sides: a, b, c — but a and b are labeled same? Wait — look closely:
- a and b are both labeled on the top two sides, but c is base.
- If a = b, then two equal sides → Isosceles
- The base angles appear equal → acute triangle
- No right angle → Acute Isosceles
- ✔ Answer: Acute Isosceles

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5)

- Sides: a, b, c — a and b are labeled, but they seem equal?
- Yes, a and b are both on the top, same length → isosceles
- The apex angle looks small → acute
- So: Acute Isosceles
- ✔ Answer: Acute Isosceles

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6)

- Two sides labeled b, one side labeled a.
- So two equal sides → Isosceles
- The angle between the two equal sides is very sharp → likely acute
- So: Acute Isosceles
- ✔ Answer: Acute Isosceles

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7)

- Has a right angle (square symbol)
- Two sides labeled a, and one side c
- So two equal legs → Right Isosceles
- ✔ Answer: Right Isosceles

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8)

- Sides: b, b, a → two equal sides → Isosceles
- The base is long, so the apex angle is wide → possibly obtuse
- Look: the base is longer than the equal sides → implies apex angle > 90° → Obtuse
- ✔ Answer: Obtuse Isosceles

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9)

- All sides labeled s → all sides equal → Equilateral
- Equilateral triangles are always acute (all angles = 60°)
- ✔ Answer: Acute Equilateral

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10)

- All sides labeled s → all equal → Equilateral
- Also acute → Acute Equilateral
- ✔ Answer: Acute Equilateral

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11)

- Two sides labeled b, one side a → two equal sides → Isosceles
- The base is short, so apex angle is narrow → acute
- So: Acute Isosceles
- ✔ Answer: Acute Isosceles

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12)

- Has a right angle (square symbol)
- Sides: a, b, c → all different labels → scalene
- So: Right Scalene
- ✔ Answer: Right Scalene

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✔ Final Answers:

| Number | Type |
|--------|--------------------|
| 1) | Right Scalene |
| 2) | Obtuse Scalene |
| 3) | Obtuse Scalene |
| 4) | Acute Isosceles |
| 5) | Acute Isosceles |
| 6) | Acute Isosceles |
| 7) | Right Isosceles |
| 8) | Obtuse Isosceles |
| 9) | Acute Equilateral |
| 10) | Acute Equilateral |
| 11) | Acute Isosceles |
| 12) | Right Scalene |

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🔍 Explanation Summary:

- Use side labels to determine if triangle is scalene, isosceles, or equilateral.
- Use angle symbols (like right-angle square) or shape appearance to determine acute, right, or obtuse.
- Remember: Equilateral → always acute.
- Right triangle → has one 90° angle (marked with square).
- Isosceles → two equal sides → two equal angles.
- Scalene → all sides and angles different.

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