Chapter 5: Q18 (page 175)

For exercises, 14-18 write paragraph proofs.
Given: parallelogram $KGLJ$ ; $FK = HL$ .
Prove: FGHJ is a parallelogram.

Short Answer

Expert verified

It is proved that the quadrilateral FGHJ is a parallelogram.

Step by step solution

Step 1. Observe the given diagram.

The given diagram is:

Step 2. Description of step.

It is being given that KGLJ is a parallelogram.

In a parallelogram, both diagonals bisect each other.

Therefore, in the parallelogram KGLJ, both diagonals KL and JG intersect each other at the point O.

Therefore, $K O = L O$ and $J O = G O$ .

Step 3. Description of step.

It is also being given that $F K = H L$ .

Therefore, it can be noticed that:

$\begin{matrix} F K = H L \\ F K + K O = H L + K O \\ F K + K O = H L + L O (∵ K O = L O) \\ F O = H O \end{matrix}$

Therefore, it can be noticed that $J O = G O$ and $F O = H O$ .

Therefore, it can be seen that the diagonals FH and JG are bisecting each other at point O.

Therefore, the quadrilateral FGHJ is a parallelogram.

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For exercises, 14-18 write paragraph proofs.
Given: parallelogram $KGLJ$ ; $FK = HL$ .
Prove: FGHJ is a parallelogram.

Short Answer

Step by step solution

Step 1. Observe the given diagram.

Step 2. Description of step.

Step 3. Description of step.

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For exercises, 14-18 write paragraph proofs.Given: parallelogram KGLJ; FK=HL.Prove: FGHJ is a parallelogram.

Short Answer

Step by step solution

Step 1. Observe the given diagram.

Step 2. Description of step.

Step 3. Description of step.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Statistics

Probability and Statistics

Theoretical and Mathematical Physics

Decision Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

For exercises, 14-18 write paragraph proofs.
Given: parallelogram $KGLJ$ ; $FK = HL$ .
Prove: FGHJ is a parallelogram.