Question

1. why is the included side important in asa triangle congruence? a. it determines the area of the triangles b. it ensures the angles form a unique triangle c. it proves that the triangles are equilateral d. it verifies the similarity of the triangles 48. which of the following represents a correct ratio if triangles are similar by sas? a. ab/de = ac/df b. ab - de = ac - df c. ab + de = ac + df d. ab de = ac df 49. what type of symmetry is shown by the logo of toyota? a. no symmetry b. translational symmetry c. rotational symmetry d. reflective symmetry

Explanation:

• For question 47: In ASA (Angle - Side - Angle) triangle congruence, the included side ensures that the two given angles form a unique triangle. Without the included side, multiple non - congruent triangles could be formed with the same two angles.
• For question 48: If two triangles are similar by SAS (Side - Angle - Side), the ratios of the corresponding sides are equal. So, if we have two similar triangles with corresponding sides AB, DE, AC, and DF, the correct ratio is $\frac{AB}{DE}=\frac{AC}{DF}$.
• For question 49: The Toyota logo has rotational symmetry. It can be rotated by certain angles and still look the same.

Answer:

1. B. It ensures the angles form a unique triangle
2. A. $AB/DE = AC/DF$
3. C. Rotational symmetry