Question

identify all the obtuse isosceles triangles.
obtuse isosceles\tnot obtuse isosceles

Explanation:

To solve this, we first recall the definitions:

• An isosceles triangle has at least two equal sides (marked by tick marks) or two equal angles.
• An obtuse triangle has one angle greater than \( 90^\circ \) (visually, one "wide" angle).

Step 1: Analyze each triangle

1. First triangle (leftmost): Two equal sides (tick marks), and one obtuse angle (visually wide).
2. Second triangle: Two equal sides, but all angles look acute (less than \( 90^\circ \)) → acute isosceles.
3. Third triangle: Right angle (marked with a square) → right isosceles, not obtuse.
4. Fourth triangle: Two equal sides, one obtuse angle → obtuse isosceles.
5. Fifth triangle: Two equal sides, all angles acute → acute isosceles.
6. Sixth triangle: Two equal sides, one obtuse angle → obtuse isosceles.

Step 2: Categorize

• Obtuse Isosceles: Triangles with two equal sides and one obtuse angle (first, fourth, sixth).
• Not Obtuse Isosceles: Triangles with two equal sides but acute angles (second, fifth) or right angle (third).

Obtuse Isosceles (drag these here):

• First triangle (two equal sides, obtuse angle)
• Fourth triangle (two equal sides, obtuse angle)
• Sixth triangle (two equal sides, obtuse angle)

Not Obtuse Isosceles (drag these here):

• Second triangle (acute isosceles)
• Third triangle (right isosceles)
• Fifth triangle (acute isosceles)

Answer:

To solve this, we first recall the definitions:

• An isosceles triangle has at least two equal sides (marked by tick marks) or two equal angles.
• An obtuse triangle has one angle greater than \( 90^\circ \) (visually, one "wide" angle).

Step 1: Analyze each triangle

1. First triangle (leftmost): Two equal sides (tick marks), and one obtuse angle (visually wide).
2. Second triangle: Two equal sides, but all angles look acute (less than \( 90^\circ \)) → acute isosceles.
3. Third triangle: Right angle (marked with a square) → right isosceles, not obtuse.
4. Fourth triangle: Two equal sides, one obtuse angle → obtuse isosceles.
5. Fifth triangle: Two equal sides, all angles acute → acute isosceles.
6. Sixth triangle: Two equal sides, one obtuse angle → obtuse isosceles.

Step 2: Categorize

• Obtuse Isosceles: Triangles with two equal sides and one obtuse angle (first, fourth, sixth).
• Not Obtuse Isosceles: Triangles with two equal sides but acute angles (second, fifth) or right angle (third).

Obtuse Isosceles (drag these here):

• First triangle (two equal sides, obtuse angle)
• Fourth triangle (two equal sides, obtuse angle)
• Sixth triangle (two equal sides, obtuse angle)

Not Obtuse Isosceles (drag these here):

• Second triangle (acute isosceles)
• Third triangle (right isosceles)
• Fifth triangle (acute isosceles)