Question

1. which theorem would explain why m∠cbd > m∠adb?

Explanation:

Step1: Analyze Triangle Sides

In $\triangle ADB$ and $\triangle CDB$, we see $AD = CB$ (marked congruent), $DB$ is common. Also, $DC = 17\,\text{cm}$ and $AB = 16\,\text{cm}$, so $DC > AB$.

Step2: Apply Angle - Side Relationship

The Hinge Theorem (SAS Inequality Theorem) states that if two sides of one triangle are congruent to two sides of another triangle, but the third side of the first triangle is longer than the third side of the second triangle, then the included angle of the first triangle is larger than the included angle of the second triangle.

In $\triangle ADB$ and $\triangle CDB$: $AD = CB$, $DB = DB$, and $DC > AB$. So, the included angle $\angle CBD$ (in $\triangle CDB$) and $\angle ADB$ (in $\triangle ADB$) satisfy $m\angle CBD>m\angle ADB$ by the Hinge Theorem.

Answer:

The Hinge Theorem (SAS Inequality Theorem)