Geometry

Which of the following are squares?

• K only

• L only

• M only

• L and M only

• All are squares

Given the figure above, identify the triangles.

• None of these are triangles

• V only

• W only

• W and X only

• V and W only

Using the statements,
Statement S: ΔABC has three sides of the same length.
Statement T: in ΔABC, ∠B and ∠C have the same measure.

Which is correct in the following statements?

• Statement S and T cannot both be true

• If S is true, the T is true

• If T is true, then S is true

• If S is false, then T is false

• None of the choices are correct.

Answer explanation

Which of the following can be called rectangles?

• All can

• Q only

• R only

• P and Q only

• Q and R only

Here are three properties of a figure.
Property D: It has diagonals of equal length
Property S: It is a square.
Property R: It is a rectangle.

Which is true in each of the following statements?

• D implies S which implies R

• S implies R which implies S

• S implies R which implies D

• R implies D which implies S

• R implies S which implies D

Answer explanation

Which of the given illustration are rectangles?

• S only

• T only

• S and T only

• S and U only

• All are rectangles

Determine the parallelograms in the given illustrations?

• J only

• L only

• J and M only

• None of these are parallelograms

• All are parallelograms

Examine these three sentences.
(1) Two lines perpendicular to the same line are parallel.
(2) A line that is perpendicular to one of two parallel lines is perpendicular to the other
(3) If two lines are equidistant, then they are parallel. In the figure below, it is given that lines m and p are perpendicular and lines n and p are perpendicular.

Which of the above sentences could be the reason that line m is parallel to line n?

• 1 only

• 2 only

• 3 only

• Either 1 or 2

• Either 2 or 3

In F-geometry, one that is different from the one you are used to, there are exactly four points and six lines. Every line contains exactly two points. If the points are P, Q, R, and S, the lines are {P, Q}, {P, R}, {P, S}, {Q, R}, {Q, S}, {R, S}

Here are how the words "intersect" and "parallel" are used in F-geometry.
- The lines {P, Q}and {P, R} intersect at P because {P, Q} and {P, R} have P in common.
- The lines {P, Q} and {R, S} are parallel because they have no points in common.

From this information, which is correct in each of the following?

• {P, R} and {Q, S} intersect

• {P, R} and {Q, S} are parallel

• {Q, R} and {R, S} are parallel

• {P, S} and {Q, R} intersect

• None of the choices are correct

What rectangles have that some parallelograms do NOT have?

• opposite sides equal

• diagonals

• opposite sides parallel

• opposite angles equal

• None of the above