Question

identify all the obtuse isosceles triangles. obtuse isosceles not obtuse isosceles

Explanation:

To solve this, we first recall the definitions:

• An isosceles triangle has at least two equal - length sides (marked by tick marks).
• An obtuse triangle has one angle greater than \(90^\circ\) (visually, it “opens wide” with one angle clearly larger than a right angle).

Step 1: Identify Isosceles Triangles

Look for triangles with tick marks (indicating equal sides):

• Triangle 1 (leftmost): Has two equal sides (tick marks) and one angle > \(90^\circ\) (obtuse).
• Triangle 2: Equilateral (all sides equal, so isosceles) but all angles \(60^\circ\) (acute, not obtuse).
• Triangle 3: Two equal sides (tick marks), angles all acute (not obtuse).
• Triangle 4: Scalene (no equal sides, so not isosceles).
• Triangle 5: Two equal sides (tick marks), angles all acute (not obtuse).
• Triangle 6: Two equal sides (tick marks) and one angle > \(90^\circ\) (obtuse).

Step 2: Classify Obtuse Isosceles

From the isosceles triangles, select those with an obtuse angle. Only the left - most triangle (Triangle 1) and the right - most triangle (Triangle 6) meet both criteria (isosceles + obtuse).

Answer:

The obtuse isosceles triangles are the first (left - most) and the sixth (right - most) triangles in the given set (the ones with two equal sides and one obtuse angle).