Question

a carpenter draws a straight line on her sketchpad and then connects different points on the line to a point above it to form a triangle. she tries it again from new points—another triangle. then again—and once more, a triangle appears. after a few tries, she pauses and thinks:
o matter how i do this, i always get a triangle.\ questions: 1. what do you notice about how all of the triangles start from the same straight line? 2. what do you wonder about the three angles inside each triangle?

Explanation:

1. All triangles share the same base (the straight line).
2. One might wonder if the sum of the three angles inside each triangle is always \(180^{\circ}\) (a fundamental property of triangles), or if the angles have any relationship based on the position of the vertex above the base line.

Answer:

1. All triangles share the same base (the straight line).
2. One might wonder if the sum of the three angles inside each triangle is always \(180^{\circ}\) (a fundamental property of triangles), or if the angles have any relationship based on the position of the vertex above the base line.