Question

question 8 of 10

if figure x is inscribed in figure y, which statement must be true?

a. figures x and y are congruent.
b. figures x and y are polygons.
c. figure y is circumscribed about figure x.
d. figure x is circumscribed about figure y.

Explanation:

Define inscribed figures

An inscribed figure is drawn inside another figure so that its vertices or boundaries touch the outer figure.

Define circumscribed figures

A circumscribed figure is drawn around another figure, touching its outer boundaries or vertices.

Analyze the relationship

If figure \(X\) is inscribed in figure \(Y\), then figure \(Y\) surrounds figure \(X\). This means figure \(Y\) is circumscribed about figure \(X\).

Evaluate the options

Using Geometric Terminology, we compare the definitions:

• Option A is false because inscribed and circumscribed figures have different sizes.
• Option B is false because the figures can be circles, which are not polygons.
• Option C is true because "inscribed in" is the dual relationship of "circumscribed about".
• Option D is false because it reverses the relationship.

Answer:

• A. Figures X and Y are congruent.
• B. Figures X and Y are polygons.
• C. Figure Y is circumscribed about figure X. (Correct answer)
• D. Figure X is circumscribed about figure Y.