Question

do you understand? mathematical practices 5. open - ended when do you think you might need to know that things are congruent in your everyday life? 6. if each angle in one triangle is congruent to its corresponding angle in another triangle, are the two triangles congruent? explain. 7. error analysis walter sketched the diagram below. he claims it shows that the two polygons are congruent. what information is missing to support his claim?

Explanation:

1. Congruence is useful in construction (matching building materials), art - for creating symmetrical designs, and in manufacturing to ensure parts fit correctly.
2. No, having congruent corresponding angles means the triangles are similar (by AA - Angle - Angle similarity criterion). For congruence, at least one pair of corresponding sides must also be congruent (e.g., ASA, SAS, SSS criteria).
3. For two polygons to be congruent, all corresponding sides and all corresponding angles must be congruent. The diagram shows some side - length markings, but there is no information about the corresponding angles being congruent.

Answer:

1. In construction, art, and manufacturing.
2. No. Having congruent corresponding angles makes triangles similar, not necessarily congruent. At least one pair of corresponding sides must also be congruent.
3. Information about the congruence of corresponding angles is missing.