Question

Consider two triangles, Triangle A and Triangle B. Triangle A has sides of length 4 cm, 5 cm, and 6 cm, while Triangle B has sides of length 6 cm, 8 cm, and 10 cm.

A. Triangle A can be proven congruent to Triangle B using SSS.
B. Triangle A can be proven congruent to Triangle B using SAS.
C. Neither SSS nor SAS can prove Triangle A congruent to Triangle B.
D. Both SSS and SAS can prove Triangle A congruent to Triangle B.

Answer 1

After analyzing the sides of the two triangles, it is found that neither SSS nor SAS congruence criteria can prove the triangles congruent due to lack of proportional sides and angle information.

Step-by-step explanation:

The question at hand involves comparing the lengths of two triangles to determine if they are congruent by either SSS (Side-Side-Side) or SAS (Side-Angle-Side) congruence criteria. Looking at Triangle A (with sides 4 cm, 5 cm, and 6 cm) and Triangle B (with sides 6 cm, 8 cm, and 10 cm), we notice that the sides of Triangle B are exactly proportionate to the sides of Triangle A by a factor of 1.5 (4x1.5 = 6, 5x1.5 = 7.5 but not 8, 6x1.5 = 9 but not 10). Because not all corresponding sides are proportionate, the triangles cannot be congruent by SSS. Additionally, without knowing any angles or knowing that either triangle is a right triangle, we cannot apply the SAS criterion either. Hence, the correct answer is C. Neither SSS nor SAS can prove Triangle A congruent to Triangle B.