Question

complete the proof that ( angle hjk cong angle ihj ).

Explanation:

Step1: Identify the given information

From the figure, we can see that the marks on the sides indicate that $\overline{IJ}\cong\overline{HK}$ (given by the markings on the sides of the quadrilateral).

Step2: Identify another pair of congruent sides

Also, from the figure, $\overline{JK}\cong\overline{HI}$ (given by the markings on the sides of the quadrilateral).

Step3: Reflexive property of congruence

For any segment $\overline{HJ}$, $\overline{HJ}\cong\overline{HJ}$ (reflexive property: a segment is congruent to itself).

Step4: Use SSS (Side - Side - Side) congruence criterion

In $\triangle HIJ$ and $\triangle JKH$, we have $\overline{IJ}\cong\overline{HK}$, $\overline{JK}\cong\overline{HI}$, and $\overline{HJ}\cong\overline{HJ}$. So, by the SSS (Side - Side - Side) congruence criterion, $\triangle HIJ\cong\triangle JKH$.

Step5: Corresponding parts of congruent triangles

Since $\triangle HIJ\cong\triangle JKH$, then $\angle HJK\cong\angle IHJ$ (corresponding parts of congruent triangles (CPCTC) are congruent).

Answer:

1. Given (from the markings on the sides of the figure)
2. Given (from the markings on the sides of the figure)
3. Reflexive property of congruence
4. SSS (Side - Side - Side) congruence criterion
5. CPCTC (Corresponding Parts of Congruent Triangles are Congruent)