Are the two triangles​ similar? If​ yes, write a similarity statement and explain how you know they are similar.

Question

Upper S
Upper B
Upper C
Upper K
Upper W
110 degrees
45 degrees
25 degrees
Question content area bottom
Part 1
Choose the correct answer below.
A.
​Yes, Upper DeltaUpper SUpper CUpper B ​~ Upper DeltaUpper KUpper CUpper W. The triangles are similar because StartFraction BC Over WC EndFraction equals StartFraction SC Over KC EndFraction equals StartFraction BS Over WK EndFraction
​, which satisfies the​ SSS~ theorem.
B.
​Yes, Upper DeltaUpper SUpper CUpper B ​~ Upper DeltaUpper KUpper CUpper W. The triangles are similar because angle Upper S congruent angle Upper K and StartFraction BC Over WC EndFraction equals StartFraction SC Over KC EndFraction
​,   which satisfies the​ SAS~ theorem.
C.
​Yes, Upper DeltaUpper SUpper CUpper B ​~ Upper DeltaUpper KUpper CUpper W. The triangles are simlar because angle Upper S congruent angle Upper K and angle SCB congruent angle WCK​, which satisfies the​ AA~ postulate.
D.
​No, the triangles are not similar because no theorem or postulate can be satisfied.

Answer 1

B. Yes, ΔSCB is similar to ΔKCW. The triangles are similar because angle S is congruent to angle K and the ratio of the corresponding side lengths BC/WC, SC/KC satisfies the SAS~ theorem.