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Example Questions
Example Question #664 : Intermediate Geometry
and are equilateral triangles that share a side . Which of the following words correctly describe Quadrilateral ?
(a) Parallelogram
(b) Rectangle
(c) Rhombus
(d) Square
(e) Trapezoid
(a) only
(e) only
(a) and (c) only
(a) and (b) only
(a), (b), (c), and (d) only
(a) and (c) only
The figure referenced is below:
is equilateral, so . is equilateral, so . By the Transitive Property of Congruence, . A quadrilateral with four congruent sides is a parallelogram and a rhombus. However, it is not a rectangle, and, consequently, not a square, since its angles are not right - , an angle of an equilateral triangle, measures . Also, a parallelogram is not a trapezoid. Therefore, the quadrilateral is a parallelogram and a rhombus only.
Example Question #21 : Equilateral Triangles
An equilateral triangle has perimeter 30.
True or false: The length of each of its midsegments is 6.
False
True
False
A midsegment of a triangle - a segment whose endpoints are the midpoints of two sides - is, by the Triangle Midsegment Theorem, parallel to the third side, and is half the length of that side. An equilateral triangle with perimeter 30 has three sides one third this, or
.
Consequently, the length of each midsegment is half this, or
.
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