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Chapter 5: Q5 (page 182)

List five ways to prove that quadrilateral ABCD is a parallelogram.

Short Answer

Expert verified

The quadrilateral ABCD is a parallelogram.

Step by step solution

01

Step 1. Apply the concept of the parallelogram.

A parallelogram is a quadrilateral with two pairs of opposite congruent and parallel sides.

02

Step 2. Step description.

The five ways to prove that a quadrilateral is a parallelogram are:

1. Prove both pairs of opposite sides are parallel.

If both the pairs of opposite sides are parallel is proven then it is a parallelogram.

2. Prove that both pairs of opposite sides are congruent.

Congruent means that their measures are the same. If both pairs of opposite sides are proven congruent then automatically both the pairs will be parallel.

3. Prove that one pair of opposite sides is both congruent and parallel.

If at least one pair of opposite sides is proven congruent and parallel then automatically the other pair will also be congruent and parallel. Hence proving the quadrilateral to be a parallelogram.

03

Step 3. Step description.

4. Prove that the diagonals of the quadrilateral bisect each other.

If the diagonals of the quadrilateral are proven to bisect each other then it is a parallelogram.

5. Prove that both pairs of opposite angles are congruent.

If both the pairs of opposite angles are proven to be congruent then the quadrilateral can be proven as a parallelogram.

Therefore, the quadrilateral is a parallelogram.

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Most popular questions from this chapter

Quadrilateral ABCD is a parallelogram. Name the principal theorem or definition that justifies the statement.

∠ADX≅∠CBX

Draw and label a diagram. List what is given and what is to be proved. Then write a two-column proof of the theorem.

Theorem 5-7.

Find something interesting to prove. Then prove it. Answers may vary.

Given: ▱ABCD;∠1≅∠2

M, N and T are the midpoints of the sides of ΔXYZ.

If XZ=10, then MN=?¯

Study the markings on each figure and decide whether ABCD must be a parallelogram. If the answer is yes, state the definition or theorem that applies.
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