Intermediate Geometry : How to find the length of the side of an equilateral triangle

Study concepts, example questions & explanations for Intermediate Geometry

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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

Possible Answers:

(a) only

(e) only

(a) and (c) only

(a) and (b) only

(a), (b), (c), and (d) only

Correct answer:

(a) and (c) only

Explanation:

The figure referenced is below:

Rhombus 1

 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.

Possible Answers:

False

True

Correct answer:

False

Explanation:

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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