Question

True or false
A) two similar triangles are always congruent.
B) two figures are similar if they have the same shape and size.
C) two triangles are similar if their corresponding sides are proportional.
D) two polygons are similar if their corresponding sides are proportional

Answer 1

Answer:

true,true,false,false

Answer 2

A)The given statement is FALSE.

• Two congruent triangles are always similar.
• But two similar triangles not necessarily be congruent.
• This is because congruency is proved only when two shapes overlap each other completely.
• But similarity depends upon proportions.
• Even if the sides are not equal, but if they are equal in proportion then two triangles are said to be similar.
• This is not the case in the congruency of two triangles.

B)The given statement is TRUE.

• As mentioned above, two congruent figures are always similar.
• So even if with the same shape and size, two figures will be similar as well as congruent.

C)The given statement is TRUE.

• According to the property of similarity of triangles, two triangles are said to be similar if their corresponding sides are proportional.
• This is because the angles of the triangles remain equal but it is only the size that changes.

D)The given statement is TRUE.

• Two polygons are said to be similar if their corresponding sides are proportional.
• But provided that both the polygons have the same number of sides.