instruction:
You are given a geometric mathematical question. Questions in this task often involve shapes and Geometric Relationships. You are also given 4 or 5 answer options (associated with "A", "B", "C", "D", "E"). Do not generate anything else apart from one of the following characters: 'A', 'B, 'C', 'D', 'E'. LaTeX mathematical format (the standard way to express mathematical expressions in the typesetting software known as LaTeX) is used to express equations. Each question is solvable with high school math knowledge.
question:
If the perimeter of equilateral triangle E equals the perimeter of square S, what is the ratio of the length of a side of square S to the length of a side of triangle E?
(A)1:1 (B)2:3 (C)3:4 (D)4:3 (E)2:1
answer:
C


question:
R, S and T are points with RT = 2RS. Which of the following could be true? I. R, S and T are the vertices of a right triangle. II. R, S and T are three of the vertices of a square. III. R, S and T all lie on the circumference of a circle.
(A)I only (B)III only (C)I and II only (D)I and III only (E)I, II, and III
answer:
D


question:
If lines \(\overline { BC } \) and \(\overline { BD } \) are each perpendicular to line \(\overline { AB } \), which of the following must be true?
(A)\(\overline { AB } \perp \overline { CD } \) (B)\(\overline { AB } \perp \overline { AC } \) (C)\(\overline { AC } \perp \overline { AD } \) (D)\(\overline { AB } \parallel \overline { CD } \) (E)\(\overline { BC } \perp \overline { BD } \)
answer:

A