Question

triangle congruence worksheet
for each pair to triangles, state the postulate or theorem that can be used to conclude that the triangles are congruent.
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triangle congruence worksheet
welch

Explanation:

Step1: Recall congruence postulates

The main triangle - congruence postulates are SSS (Side - Side - Side), SAS (Side - Angle - Side), ASA (Angle - Side - Angle), AAS (Angle - Angle - Side), and HL (Hypotenuse - Leg for right - triangles).

Step2: Analyze each pair of triangles

For each pair, identify the marked congruent sides and angles.

1. In triangle FGI and triangle HGI, we have FI = HI, ∠FIG=∠HIG, and GI = GI. So, by SAS (Side - Angle - Side), the triangles are congruent.
2. In triangle ONQ and triangle OPQ, we have ON = OP, NQ = PQ, and OQ = OQ. So, by SSS (Side - Side - Side), the triangles are congruent.
3. In triangle ABC and triangle DEC, we have ∠ACB = ∠DCE, BC = EC, and ∠ABC=∠DEC. So, by ASA (Angle - Side - Angle), the triangles are congruent.
4. In triangle RSU and triangle TSU, we have ∠RSU = ∠TSU, SU = SU, and ∠RUS=∠TUS. So, by ASA (Angle - Side - Angle), the triangles are congruent.
5. In triangle JKM and triangle LKM, we have ∠J = ∠L, ∠JMK = ∠LMK, and MK = MK. So, by AAS (Angle - Angle - Side), the triangles are congruent.
6. In triangle ONP and triangle QNP, we have ∠ONP = ∠QNP, NP = NP, and ∠OPN=∠QPN. So, by ASA (Angle - Side - Angle), the triangles are congruent.
7. In triangle ABC and triangle DEC, we have ∠ACB = ∠DCE, ∠BAC = ∠EDC, and BC = EC. So, by AAS (Angle - Angle - Side), the triangles are congruent.
8. In triangle FGI and triangle HGI, we have ∠FIG = ∠HIG, ∠FGI=∠HGI, and GI = GI. So, by ASA (Angle - Side - Angle), the triangles are congruent.
9. In triangle JKM and triangle LKM, we have JK = LK, ∠JKM = ∠LKM, and KM = KM. So, by SAS (Side - Angle - Side), the triangles are congruent.
10. In triangle ONP and triangle QNP, we have ∠ONP = ∠QNP, ∠OPN = ∠QPN, and NP = NP. So, by ASA (Angle - Side - Angle), the triangles are congruent.
11. In triangle JKM and triangle LKM, we have ∠J = ∠L, ∠JKM = ∠LKM, and KM = KM. So, by AAS (Angle - Angle - Side), the triangles are congruent.
12. In triangle RSU and triangle TSU, we have RS = TS, SU = SU, and RU = TU. So, by SSS (Side - Side - Side), the triangles are congruent.

Answer:

1. SAS
2. SSS
3. ASA
4. ASA
5. AAS
6. ASA
7. AAS
8. ASA
9. SAS
10. ASA
11. AAS
12. SSS