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In this lesson, we will learn how to correlate the measurements of the side lengths of two triangles with the angle measures in each triangle.

Q1:

Consider the two triangles in the diagram.

Length π is equal to length π and length π is equal to length π . Given that the perimeter of triangle 1 is less than the perimeter of triangle 2, what does the converse of the hinge theorem tell us about the measures of angles π and π ?

Q2:

In the triangles, using the converse of the hinge theorem, determine whether π is greater than, less than, or equal to π .

Q3:

Consider the triangles π΄ π΅ πΆ and π· πΈ πΉ , where π΄ π΅ = π· πΈ and π΅ πΆ = πΈ πΉ . Given that π΄ πΆ > π· πΉ and using the converse of the Hinge theorem, determine whether β π΄ π΅ πΆ is greater than β π· πΈ πΉ .

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