Question

determine if the two triangles are necessarily congruent. if so, fill in a flowchart proof to prove that they are.

the triangles ~ necessarily congruent.

answer attempt 2 out of 2
you must answer all questions above in order to submit.

Explanation:

Step1: Identify given congruent parts

In $\triangle XYW$ and $\triangle KIJ$:

• $XY = IJ$ (marked with one tick)
• $YW = KI$ (marked with two ticks)
• $\angle Y = \angle I$ (marked as equal angles)

Step2: Apply SAS congruence criterion

The Side - Angle - Side (SAS) congruence criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

For $\triangle XYW$ and $\triangle KIJ$:

• Side $XY$ (of $\triangle XYW$) $\cong$ Side $IJ$ (of $\triangle KIJ$)
• Included angle $\angle Y$ (of $\triangle XYW$) $\cong$ Included angle $\angle I$ (of $\triangle KIJ$)
• Side $YW$ (of $\triangle XYW$) $\cong$ Side $KI$ (of $\triangle KIJ$)

By the SAS congruence postulate, $\triangle XYW\cong\triangle KIJ$. So the triangles are necessarily congruent.

Answer:

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