can you help me with this question

Question

Given that ΔABC is similar to ΔGHJ, which of the following statements must be true?

a	Both triangles have the same side lengths.
b	If ΔABC has a right angle, then ΔGHJ has a right angle.
c	The perimeter of ΔABC is greater than the perimeter of ΔGHJ.
d	If ΔABC has a side of length 2 cm, then ΔGHJ has a side of length 2 cm.

Answer 1

Hi Chandreka,

Triangles are similar if their corresponding angles are congruent and the corresponding sides are in proportion. In other words, similar triangles are the same shape but not necessarily the same size.

a. We do not know this for sure. Not necessarily the same size.	Both triangles have the same side lengths.
b. True. Corresponding angles are congruent.	If ΔABC has a right angle, then ΔGHJ has a right angle.
c. We do not know this for sure. Not necessarily the same size.	The perimeter of ΔABC is greater than the perimeter of ΔGHJ.
d. We do not know this for sure. Not necessarily the same size.	If ΔABC has a side of length 2 cm, then ΔGHJ has a side of length 2 cm.

Answer 2

So similar triangles have the same angles and their sides are proportional, but not necessarily the same size (although it is possible). Because they don't need to have the same size that rules out a and d. Then they tell us nothing about the sizes of the triangles - just that they are similar. Thus, we don't know anything about their perimeters and c cannot be true. So according to the definition of similarity - same angles and proportional sides - letter B has to be correct.