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Chapter 5: Q. 4 (page 199)

Complete the following statement with the word always, sometimes, or never.

A rhombus is ___ a parallelogram.

Short Answer

Expert verified

A rhombus is alwaysa parallelogram.

Step by step solution

01

Step 1- Apply the concept of parallelogram and rhombus.

A parallelogram is a quadrilateral with opposite sides parallel and therefore congruent as well as opposite angles congruent.

A rhombus is a quadrilateral with all sides equal and opposite angles are congruent.

02

Step 2- Step description.

Since a rhombus is a quadrilateral with all sides congruent and opposite angles congruent and also a parallelogram is a quadrilateral with opposite sides parallel and therefore congruent as well as opposite angles congruent.

Therefore, a rhombus possesses all the properties of a parallelogram.

03

Step 3- Step description.

Since a rhombus possesses all the properties of a parallelogram thus a rhombus is always a parallelogram.

Therefore, a rhombus is always a parallelogram.

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Most popular questions from this chapter

The coordinates of three vertices of parallelogram ABCD are given. Plot the points and find the coordinates of the fourth vertex.

A(3,2),B(8,2),C(?,?),D(0,5)

Write a paragraph proof: The sum of the lengths of the segments drawn from any point in the base of an isosceles triangle perpendicular to the legs is equal to the length of the altitude drawn to one leg.

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Prove: localid="1637661691185" AB¯≅CE¯

For exercises, 14-18 write paragraph proofs.

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