Question

row 1
two triangles are always similar.
true
false
row 2
two isosceles triangles are always similar.
true
false
row 3
two equilateral triangles are always similar.
true
false

Explanation:

Row 1:

Step1: Recall triangle similarity

Two triangles are similar if their corresponding angles are equal. For any two triangles, if we don't know their angle measures, they aren't always similar. So "Two triangles are ALWAYS similar" is false.

Step2: Evaluate the statement

Since not all pairs of triangles have equal corresponding angles, the statement is false.

Row 2:

Step1: Recall isosceles triangle angles

Isosceles triangles have two equal angles, but the angle measures can vary (e.g., one isosceles triangle with angles \(30^\circ, 30^\circ, 120^\circ\) and another with \(40^\circ, 40^\circ, 100^\circ\) are not similar). So two isosceles triangles aren't always similar.

Step2: Evaluate the statement

Since angle measures can differ, the statement is false.

Row 3:

Step1: Recall equilateral triangle angles

All equilateral triangles have angles of \(60^\circ\) each. By AA (Angle - Angle) similarity criterion, if two triangles have two pairs of equal angles, they are similar. For equilateral triangles, all three angles are equal (\(60^\circ\)), so corresponding angles are equal.

Step2: Evaluate the statement

Since all equilateral triangles have equal angles, they are always similar. So the statement is true.

Answer:

• Row 1: False
• Row 2: False
• Row 3: True