Question

If two isosceles triangles are constructed on the same base, prove that the line joining the two vertices forms two congruent triangles.

Answer 1

To prove that the line joining the two vertices of two isosceles triangles constructed on the same base forms two congruent triangles, we can use the property of isosceles triangles that their base angles are congruent and their sides opposite to those angles are congruent.

Step-by-step explanation:

To prove that the line joining the two vertices of two isosceles triangles constructed on the same base forms two congruent triangles, we can use the property of isosceles triangles that their base angles are congruent and their sides opposite to those angles are congruent.

1. Construct two isosceles triangles ABC and A'B'C' on the same base AB.
2. Since the triangles are isosceles, we have AB = AC and A'B' = A'C'.
3. Draw the line segment joining the vertices A and A'.
4. By construction, we have AA' as the line joining the two vertices.
5. Since AB = A'B' and AC = A'C', and we know that two sides and the included angle of a triangle are congruent to the corresponding sides and included angle of another triangle, we can conclude that the triangles ABC and A'B'C' are congruent.

Therefore, the line joining the two vertices of the two isosceles triangles forms two congruent triangles.