Triangle Congruence Postulates

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📚 Part 1: Identifying Triangle Congruence Postulates

1. Which postulate proves that two triangles are congruent if all three pairs of corresponding sides are equal?

SSS (Side-Side-Side)

SAS (Side-Angle-Side)

ASA (Angle-Side-Angle)

AAS (Angle-Angle-Side)

2. For the SAS postulate, what must be equal between two triangles?

Two sides and any angle

Two sides and the included angle

Two angles and any side

Three sides

3. In the ASA postulate, what does "included side" mean?

The longest side of the triangle

The side between two given angles

Any side of the triangle

The side opposite to the largest angle

4. Triangle ABC has sides AB = 5 inches, BC = 7 inches, and AC = 9 inches. Triangle DEF has sides DE = 5 inches, EF = 7 inches, and DF = 9 inches. Which postulate proves these triangles are congruent?

SSS

SAS

ASA

Cannot be determined

✏️ Part 2: Applying Congruence Postulates

5. Given: Triangle PQR where PQ = 8 cm, angle Q = 60°, and QR = 6 cm. Triangle XYZ where XY = 8 cm, angle Y = 60°, and YZ = 6 cm. Which postulate proves these triangles are congruent? ________________ Explain your reasoning:

6. A construction worker needs to verify that two triangular supports are identical. He measures: Support 1: All three sides measure 12 feet, 15 feet, and 18 feet Support 2: All three sides measure 12 feet, 15 feet, and 18 feet Can he conclude the supports are congruent? Which postulate applies?

7. Fill in the blanks with the correct postulate (SSS, SAS, or ASA): a) Two sides and the included angle are equal: __________ b) All three corresponding sides are equal: __________ c) Two angles and the included side are equal: __________

🔍 Part 3: Problem Solving

8. Triangle ABC ≅ Triangle DEF. Given that AB = DE = 10 cm, BC = EF = 8 cm, and angle B = angle E = 45°. Which congruence postulate was used? Justify your answer by explaining why the other postulates don't apply.

9. Draw and label two congruent triangles that could be proven congruent using the ASA postulate. Include all necessary measurements and markings.