Question

which of the following pairs show(s) triangles that are similar but not congruent? a b c a, b, and c a and c only b only b and c only

Explanation:

Step1: Check similarity and congruence for A

For pair A, by AA (Angle - Angle) similarity criterion (two angles are equal), triangles are similar. But side lengths are different (visually from the figure), so not congruent.

Step2: Check similarity and congruence for B

For pair B, using Pythagoras: First triangle has sides \(a,b,c\) where \(c=\sqrt{a^{2}+b^{2}}\), second triangle has sides \(a',b',c'\) where \(c'=\sqrt{a'^{2}+b'^{2}}\). Here \(a = 3,b = 4,c = 5\) and \(a'=4,b'=4,c'=\sqrt{32}\). They are not similar (ratios of sides \(\frac{3}{4}
eq\frac{4}{4}
eq\frac{5}{\sqrt{32}}\))

Step3: Check similarity and congruence for C

For pair C, by AA (Angle - Angle) similarity criterion (two angles are equal), triangles are similar. But side lengths are different (visually from the figure), so not congruent.

Answer:

B. A and C only