Question

when two triangles are similar, their corresponding sides are:
a. perpendicular
b. parallel
c. equal
d. proportional

which term describes triangles that have the same shape but different sizes?
a. similar
b. congruent
c. identical
d. parallel

Explanation:

First Question (When two triangles are similar, their corresponding sides are: )

To solve this, we recall the definition of similar triangles. Similar triangles have corresponding angles equal and corresponding sides in proportion (i.e., the ratios of corresponding sides are equal). Let's analyze each option:

• Option a: Perpendicular sides are related to angle measure (90 degrees), not a property of similar triangle sides. Eliminate.
• Option b: Parallel sides are about the orientation of lines, not a property of similar triangle sides. Eliminate.
• Option c: Equal sides are a property of congruent triangles (same shape and size), not similar (which can be different sizes). Eliminate.
• Option d: Proportional sides match the definition of similar triangles.

We analyze each option based on triangle definitions:

• Option a: Similar triangles are defined as having the same shape (corresponding angles equal) but can have different sizes (corresponding sides proportional). This matches.
• Option b: Congruent triangles have the same shape and size (corresponding sides equal, angles equal). Eliminate.
• Option c: Identical triangles are the same as congruent, same shape and size. Eliminate.
• Option d: Parallel is a property of lines, not a triangle classification term. Eliminate.

Answer:

d. Proportional

Second Question (Which term describes triangles that have the same shape but different sizes? )