Question

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

Explanation:

To identify obtuse isosceles triangles, we use the definitions:

• Isosceles triangle: Has at least 2 equal sides (marked by tick marks) or 2 equal angles.
• Obtuse triangle: Has one angle greater than \( 90^\circ \) (visually, a "wide" angle).

Step 1: Analyze each triangle

1. First triangle (leftmost):

• Equal sides (tick marks on 2 sides) → isosceles.
• One angle is clearly greater than \( 90^\circ \) → obtuse.
• Classify: Obtuse Isosceles.

1. Second triangle:

• Equal sides (tick marks on 2 sides) → isosceles.
• All angles appear acute (less than \( 90^\circ \)) → acute, not obtuse.
• Classify: Not Obtuse Isosceles.

1. Third triangle (right angle):

• Equal sides (tick marks on 2 sides) → isosceles (right isosceles triangle).
• One angle is \( 90^\circ \) (right angle), not obtuse (\( >90^\circ \)) → not obtuse.
• Classify: Not Obtuse Isosceles.

1. Fourth triangle:

• Equal sides (tick marks on 2 sides) → isosceles.
• One angle is greater than \( 90^\circ \) → obtuse.
• Classify: Obtuse Isosceles.

1. Fifth triangle:

• Equal sides (tick marks on 2 sides) → isosceles.
• All angles appear acute → acute, not obtuse.
• Classify: Not Obtuse Isosceles.

1. Sixth triangle:

• No equal sides (no tick marks) → scalene (not isosceles) → automatically not obtuse isosceles.
• Classify: Not Obtuse Isosceles.

Step 2: Organize into columns

• Obtuse Isosceles: First triangle, Fourth triangle.
• Not Obtuse Isosceles: Second, Third, Fifth, Sixth triangles.

Answer:

Obtuse Isosceles	Not Obtuse Isosceles