Question

geometry support unit 2-triangle congruence notes practice: determine whether there is enough information to say the triangles are congruent. if so, state the congruence theorem (sss, sas, asa, aas, hl). if not, write not congruent. remember, the only markings you can add to a picture are vertical angles or a reflexive side. 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12)

Explanation:

Step1: Analyze the first pair of triangles

Check for congruence theorems. There are three pairs of equal sides (SSS - Side - Side - Side).

Step2: Analyze the second pair of triangles

The side - side - side (SSS) condition is not met as the side lengths do not match in the correct order.

Step3: Analyze the third pair of triangles

There are two angles and a non - included side (AAS - Angle - Angle - Side).

Step4: Analyze the fourth pair of triangles

Right triangles with hypotenuse and leg (HL - Hypotenuse - Leg).

Step5: Analyze the fifth pair of triangles

Two sides and included angle (SAS - Side - Angle - Side).

Step6: Analyze the sixth pair of triangles

Two angles and included side (ASA - Angle - Side - Angle).

Step7: Analyze the seventh pair of triangles

Two angles and non - included side (AAS).

Step8: Analyze the eighth pair of triangles

Two angles and included side (ASA).

Step9: Analyze the ninth pair of triangles

Three pairs of equal sides (SSS).

Step10: Analyze the tenth pair of triangles

Two sides and included angle (SAS).

Step11: Analyze the eleventh pair of triangles

Two sides and included angle (SAS).

Step12: Analyze the twelfth pair of triangles

Three pairs of equal sides (SSS).

Answer:

1. SSS
2. not congruent
3. AAS
4. HL
5. SAS
6. ASA
7. AAS
8. ASA
9. SSS
10. SAS
11. SAS
12. SSS