Converse of Hinge Theorem - Inequality Between Two Triangles

Introduction to the Converse of the Hinge Theorem00:00:00

Teacher Gon introduces the video, which will discuss the Converse of the Hinge Theorem. The video contrasts this with a previous video on the Hinge Theorem. Viewers are encouraged to like, subscribe, and hit the bell for updates.

Statement of the Converse of the Hinge Theorem00:00:40

The theorem states that if two sides of one triangle are congruent to two sides of another triangle, and the third side of the first triangle is longer than the third side of the second, then the included angle in the first triangle is greater than the included angle in the second triangle.

Example 1: Comparing Angles A and D00:01:39

Using triangles ABC and DEF, where two sides are congruent and side BC is longer than side EF, it is determined that angle A (opposite BC) is greater than angle D (opposite EF).

Example 2: Comparing Angles ANL and RNL00:03:10

In triangles ANL and RNL, sides AN and RN are congruent, and side LN is shared (making it congruent in both). Since side RL (7 units) is longer than side AL (4 units), the angle opposite RL (angle ANL) is less than the angle opposite AL (angle RNL).

Conclusion and Call to Action00:04:44

The video concludes by summarizing the concept of the Converse of the Hinge Theorem. Viewers are invited to suggest future topics in the comment section and are reminded to like, subscribe, and hit the notification bell for new uploads.