Question

1. state what information is needed in order to make the given sss congruent reason true.
2. state what information is needed in order to make the given aas congruent reason true.
3. state what information is needed in order to make the given sss congruent reason tr
4. state what information is needed in order to make the given sss congruent reason tr
5. state what information is needed in order to make the given aas congruent reason th
6. state what information is needed in order to make the given aas congruent reason true.
7. state what information is needed in order to make the given sas congruent reason true.

Explanation:

Problem 8 (SSS):

Step1: Identify existing congruent sides

We know $\overline{JI} \cong \overline{FE}$, $\overline{JK} \cong \overline{FG}$.

Step2: Find missing side for SSS

SSS requires 3 congruent side pairs. Missing pair: $\overline{IK} \cong \overline{EG}$

Problem 9 (AAS):

Step1: Identify existing congruent parts

We know $\angle B \cong \angle H$, $\angle A \cong \angle G$.

Step2: Find missing part for AAS

AAS requires 2 angles + 1 non-included side. Missing pair: $\overline{BC} \cong \overline{HI}$ or $\overline{AC} \cong \overline{GI}$

Problem 10 (SSS):

Step1: Identify existing congruent sides

We know $\overline{LM} \cong \overline{QM}$, $\overline{LK} \cong \overline{QK}$.

Step2: Find missing side for SSS

SSS requires 3 congruent side pairs. Missing pair: $\overline{MK} \cong \overline{MK}$ (common side, already congruent, or confirm $\overline{LM} \cong \overline{QM}$, $\overline{LK} \cong \overline{QK}$, so the third side is shared, but if needing a stated pair, $\overline{MK} \cong \overline{MK}$)

Problem 11 (SSS):

Step1: Identify existing congruent sides

We know $\overline{UW} \cong \overline{YW}$, $\overline{UX} \cong \overline{YX}$.

Step2: Find missing side for SSS

SSS requires 3 congruent side pairs. Missing pair: $\overline{WX} \cong \overline{WX}$ (common side, already congruent, or $\overline{UW} \cong \overline{YW}$, $\overline{UX} \cong \overline{YX}$, so third side $\overline{WX}$ is shared)

Problem 12 (AAS):

Step1: Identify existing congruent parts

We know $\angle S \cong \angle X$, $\overline{ST} \cong \overline{XW}$.

Step2: Find missing part for AAS

AAS requires 2 angles + 1 non-included side. Missing pair: $\angle T \cong \angle W$ or $\angle R \cong \angle Y$

Problem 13 (AAS):

Step1: Identify existing congruent parts

We know $\angle H \cong \angle C$, $\overline{IJ} \cong \overline{AB}$.

Step2: Find missing part for AAS

AAS requires 2 angles + 1 non-included side. Missing pair: $\angle I \cong \angle A$ or $\angle J \cong \angle B$

Problem 14 (SAS):

Step1: Identify existing congruent parts

We know $\overline{SR} \cong \overline{JI}$, $\angle S \cong \angle J$.

Step2: Find missing part for SAS

SAS requires 2 sides + included angle. Missing pair: $\overline{ST} \cong \overline{JK}$

Answer:

1. Problem 8: $\overline{IK} \cong \overline{EG}$
2. Problem 9: $\overline{BC} \cong \overline{HI}$ (or $\overline{AC} \cong \overline{GI}$)
3. Problem 10: $\overline{MK} \cong \overline{MK}$ (common side, or confirm the shared side is congruent)
4. Problem 11: $\overline{WX} \cong \overline{WX}$ (common side, or confirm the shared side is congruent)
5. Problem 12: $\angle T \cong \angle W$ (or $\angle R \cong \angle Y$)
6. Problem 13: $\angle I \cong \angle A$ (or $\angle J \cong \angle B$)
7. Problem 14: $\overline{ST} \cong \overline{JK}$