Question

If stu abc, which congruences are true by CPCTC? Check all that apply.

a. st ≅ ac
b. s ≅ a
c. u ≅ b
d. t ≅ b
e. tu ≅ bc
f. su ≅ bc
Options:
Option 1: a, b, c, d, e, f
Option 2: a, c, e
Option 3: b, d, f
Option 4: a, b, c, d
Option 5: c, e, f

Answer 1

By applying CPCTC, congruences a (st ≅ ac), b (s ≅ a), c (u ≅ c), and e (tu ≅ bc) are true, with congruences d and f being incorrect.

Step-by-step explanation:

The principle of CPCTC (Corresponding Parts of Congruent Triangles are Congruent) is used to determine which parts of congruent triangles are equal to each other. If triangles STU and ABC are congruent (triangle STU ≅ triangle ABC), then each corresponding side and angle of the first triangle is congruent to the corresponding side and angle of the second triangle.

• a. st ≅ ac: This is true because side ST of triangle STU corresponds to side AC of triangle ABC.
• b. s ≅ a: This is also true because angle S of triangle STU corresponds to angle A of triangle ABC.
• c. u ≅ c: This is true because angle U of triangle STU corresponds to angle C of triangle ABC.
• d. t ≅ b: This is not true because angle T of triangle STU does not correspond to angle B of triangle ABC.
• e. tu ≅ bc: This is true because side TU of triangle STU corresponds to side BC of triangle ABC.
• f. su ≅ bc: This is not true because side SU of triangle STU does not correspond to side BC of triangle ABC.

Therefore, the congruences that are true by CPCTC are a, b, c and e.