Answer:
To experimentally verify that the base angles of an isosceles triangle are equal, we will need two isosceles triangles of different sizes.
Materials needed:
Two sheets of paper
Ruler
Pencil
Protractor
Scissors
Experiment:
Draw a large isosceles triangle on one sheet of paper by drawing a straight line at least 20 cm long. Then draw two additional lines from each end of the first line to meet at the top, forming an isosceles triangle. Label the base as "AB" and the other two sides as "AC" and "BC."
Measure and mark the midpoint of the base "AB."
Using a ruler, draw a perpendicular bisector through the midpoint of the base. This line should create two congruent segments.
Measure each angle formed by the intersection of the perpendicular bisector and the two sides of the triangle. Use a protractor to measure these angles.
Repeat steps 1-4 with a smaller isosceles triangle on the second sheet of paper. The smaller triangle should have a base of at least 10 cm and two sides of equal length.
Compare the measurements of the angles of both triangles. If the triangles are truly isosceles, then the two angles opposite the base (ACB) should measure the same in both triangles.
Cut out both isosceles triangles along their outlines.
Fold each triangle along the perpendicular bisector line drawn in step 3 so that the two congruent segments come together.
If the angles opposite the base are indeed equal, then the two sides of each triangle should match up perfectly when folded along the perpendicular bisector. If they do not match up, then the triangles are not truly isosceles.
By repeating this experiment with different sized isosceles triangles, we can verify that the base angles of any isosceles triangle are always equal.