Answers to True and False Questions on Exam 2 Review
True or False. Justify your answer.
A. Every isosceles triangle is equilateral.
False. Some isosceles triangles are equilateral, since a
triangle with three congruent sides is both isosceles and
equilateral.
B. All equilateral triangles are isosceles.
True. If a triangle has three congruent sides then it
certainly has two congruent sides.
C. All squares are rectangles.
True. One of the definitions of a square is that it is a
rectangle with all sides congruent. Hence, every square,
by definition, is a rectangle.
D. Some rectangles are rhombuses.
True. Since a square is both a rectangle and a rhombus,
squares are rectangles that are rhombuses.
E. Every rhombus is a regular quadrilateral.
False. A regular polygon has congruent sides and
congruent angles. A rhombus has congruent sides,
but not necessarily congruent angles. However, some
rhombuses are regular polygons. For example, a square
is a rhombus and also a regular quadrilateral.
F. Some rectangles are squares.
True. Squares are defined to be those rectangles that have
four right angles.
G. Some right triangles are isosceles.
True. One can draw a right triangle with congruent
legs as an explanation for why this is a true statement.
H. Every parallelogram is a trapezoid.
True if you use the definition of a trapezoid from our book.
It says that a trapezoid is a quadrilateral with at least one
pair of opposite sides parallel. Since a parallelogram has
two pair of opposite sides parallel, it is a trapezoid.
However, most books (and most people) define a trapezoid
To be a quadrilateral with exactly one pair of opposite sides
Parallel. Using this definition, no parallelogram is a
trapezoid.
I. All parallelograms are quadrilaterals.
True. It is part of the definition of a parallelogram.
J. Every parallelogram is a trapezoid.
(Duplicate question to H.)
K. Every equilateral triangle is a scalene triangle.
False. No equilateral triangle is scalene. A scalene
triangle has no pair of sides congruent. An equilateral
triangle has all thee sides congruent.
L. Every square is a kite.
True. A square has all of its sides congruent. Therefore
distinct pairs of consecutive sides are congruent.
M. No square is a rectangle.
False. All squares are rectangles by the definition of a
square.