Question

scenario 1

1. solomon says: i have drawn a triangle. it has one angle of 30° and another angle of 40°. adeline, you draw a triangle with the same two properties.

adeline says: my triangle will be congruent to yours because all triangles that have those two properties must be congruent.
is adeline correct to say that all triangles with these two properties must be congruent? explain your answer.
adeline is not correct. triangles

scenario 2

1. evan says: i have drawn a triangle. it has one right angle, and one side is 1 inch long. suzie, you draw a triangle with the same two properties.

suzie says: my triangle will be congruent to yours because all triangles that have those two properties must be congruent.
is suzie correct to say all triangles with these two properties must be congruent? explain your answer.

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Explanation:

Scenario 1

Step1: Recall congruence criteria

Congruent triangles require SSS (side - side - side), SAS (side - angle - side), ASA (angle - side - angle), AAS (angle - angle - side) or HL (hypotenuse - leg for right - triangles). Knowing only two angles (30° and 40°) gives the third angle as 180°-(30° + 40°)=110°, but no information about side lengths. Different side - length combinations can form non - congruent triangles with the same angle measures (similar triangles).

Step2: Conclusion

Adeline is incorrect. Triangles with just two known angles are not necessarily congruent.

Scenario 2

Step1: Analyze given information

We know one right angle and one side length of 1 inch. But we don't know if the 1 - inch side is a leg or the hypotenuse. Also, we have no information about the other sides or non - right angles.

Step2: Conclusion

Suzie is incorrect. Different triangle configurations can have a right angle and a 1 - inch side without being congruent.

Answer:

1. Adeline is not correct. Triangles with two given angles are not necessarily congruent as side - lengths are not specified.
2. Suzie is not correct. With a right angle and one side length given, without more information about side positions and other elements, triangles are not necessarily congruent.