Question

skills practice #22: congruent triangles proofs - sss and sas
directions: state whether the triangles can be proven congruent, if possible, by sss or sas.
include a congruency statement for all congruent triangles.
1
2
3
4
5
6
7
8

Explanation:

Step1: Analyze Triangle 1 (SSS)

Identify 3 congruent sides: $QY \cong EC$, $TF \cong KP$, $QT \cong EP$. By SSS, $\triangle QTF \cong \triangle EPC$.

Step2: Analyze Triangle 2 (SSS)

Identify 3 congruent sides: $AB \cong DC$, $AD \cong BC$, $AC \cong CA$. By SSS, $\triangle ABC \cong \triangle CDA$.

Step3: Analyze Triangle 3 (SAS)

Identify 2 sides, included angle: $JM \cong LK$, $\angle JMK \cong \angle LKM$, $MK \cong KM$. By SAS, $\triangle JMK \cong \triangle LKM$.

Step4: Analyze Triangle 4 (SAS)

Identify 2 sides, included angle: $SU \cong TU$, $\angle SUV \cong \angle TUW$, $UV \cong UW$. By SAS, $\triangle SUV \cong \triangle TUW$.

Step5: Analyze Triangle 5 (SSS)

Identify 3 congruent sides: $CE \cong DE$, $CF \cong DF$, $EF \cong EF$. By SSS, $\triangle CEF \cong \triangle DEF$.

Step6: Analyze Triangle 6 (SAS)

Identify 2 sides, included angle: $JA \cong MA$, $\angle JAD \cong \angle MAE$, $DA \cong EA$. By SAS, $\triangle JAD \cong \triangle MAE$.

Step7: Analyze Triangle 7 (SAS)

Identify 2 sides, included angle: $PQ \cong TU$, $\angle Q \cong \angle T$, $QR \cong TU$. By SAS, $\triangle PQR \cong \triangle TSU$.

Step8: Analyze Triangle 8 (SAS)

Identify 2 sides, included angle: $AB \cong ED$, $\angle ACB \cong \angle ECD$, $BC \cong DC$. By SAS, $\triangle ABC \cong \triangle EDC$.

Answer:

1. Congruent by SSS; $\triangle QTF \cong \triangle EPC$
2. Congruent by SSS; $\triangle ABC \cong \triangle CDA$
3. Congruent by SAS; $\triangle JMK \cong \triangle LKM$
4. Congruent by SAS; $\triangle SUV \cong \triangle TUW$
5. Congruent by SSS; $\triangle CEF \cong \triangle DEF$
6. Congruent by SAS; $\triangle JAD \cong \triangle MAE$
7. Congruent by SAS; $\triangle PQR \cong \triangle TSU$
8. Congruent by SAS; $\triangle ABC \cong \triangle EDC$