Question

prove ∠h≅∠t by filling out the flowchart below. for each box, choose a statement format from the dropdown menu. you will then be able to letters to match the diagram for this problem.

Explanation:

Step1: Identify congruent sides

In \(\triangle TUV\) and \(\triangle HFG\), we have \(TU = HF\), \(TV=HG\) and \(UV = FG\) (from the markings on the sides of the triangles).

Step2: Apply SSS - Side - Side - Side congruence criterion

If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. So, \(\triangle TUV\cong\triangle HFG\) by SSS congruence.

Step3: Use corresponding - parts of congruent triangles are congruent (CPCTC)

Since \(\triangle TUV\cong\triangle HFG\), then \(\angle H\cong\angle T\) because they are corresponding angles of congruent triangles.

Answer:

By showing \(\triangle TUV\cong\triangle HFG\) using SSS congruence and then applying CPCTC, we prove \(\angle H\cong\angle T\).