Question

directions: classify the triangles as isosceles, scalene or equilateral (some triangles may be classified as more than one category).
1.
2.
3.
4.
directions: classify the triangles as acute, obtuse or right.
1.
2.

Explanation:

Step1: Classify triangle 1 by sides

All 3 sides are equal (4cm each). A triangle with all equal sides is equilateral, and equilateral triangles are also a type of isosceles triangle (since isosceles requires at least 2 equal sides).

Step2: Classify triangle 2 by sides

Two sides are equal (9ft each), one side is different (13ft). A triangle with exactly two equal sides is isosceles.

Step3: Classify triangle 3 by sides

All 3 sides are different (3in, 6in, 7in). A triangle with no equal sides is scalene.

Step4: Classify triangle 4 by sides

Two sides are equal (8mm each), one side is different (4mm). A triangle with exactly two equal sides is isosceles.

Step5: Classify angle triangle 1

All angles are less than $90^\circ$ ($42^\circ$, $77^\circ$, $61^\circ$). A triangle with all acute angles is acute.

Step6: Classify angle triangle 2 (incomplete note correction)

The given angle is $41^\circ$, but the partial "Right" note is incorrect. However, using the sum of angles: if we assume the missing angles sum to $139^\circ$, but since only one angle is shown, we use the definition: if no angle is $90^\circ$ or $>90^\circ$ from the visible info, but wait—wait, the visible angle is acute, but the partial "Right" is wrong. Wait, no: the sum of angles in a triangle is $180^\circ$. If one angle is $41^\circ$, the other two sum to $139^\circ$. But since the handwritten note says "acute", that implies all angles are acute. Wait, no—correction: the first angle triangle has all angles acute, so it's acute. For the second angle triangle, with one $41^\circ$ angle, if the other two are acute (sum to $139^\circ$, so each can be less than $90^\circ$ e.g., $80^\circ$ and $59^\circ$), so it is acute (matching the handwritten note).

Answer:

1. Equilateral, Isosceles
2. Isosceles
3. Scalene
4. Isosceles

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Angle Classification:

1. Acute triangle
2. Acute triangle