Chapter 5: Q8 (page 182)

Given that $▱ P Q R S$ , where $\bar{P X}$ bisects $∠ Q P R$ , $\bar{R Y}$ bisects $∠ S R P$ . Then prove that $R Y P X$ is a parallelogram.

Short Answer

Expert verified

Therefore, RYPX is a parallelogram.

Step by step solution

Step 1. Check the figure.

Consider the figure.

Step 2. Step description.

Consider that PQRS is a parallelogram. Thus, the line PS is parallel to the line RQ.

Hence the line PY is parallel to the line RX.

By the alternate interior angle theorem, it is clear that $∠ Q P R = ∠ S R P$ …... (1)

Step 3. Step description.

Consider the angles $∠ Q P R$ and $∠ S R P$ . Thus, from the figure

$∠ S R P = 2 ∠ Y R P$

$∠ Q P R = 2 ∠ X P R$

Use the equation (1) as follows:

$\begin{array}{l} 2 ∠ X P R = 2 ∠ Y R P \\ ∠ X P R = ∠ Y R P \end{array}$

Now, the angles $∠ X P R$ and $∠ Y R P$ are the alternate interior angles for the line $R Y, P X$ .

Thus, the lines $R Y, P X$ are parallel.

Therefore, RYPX is a parallelogram.

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Given that $▱ P Q R S$ , where $\bar{P X}$ bisects $∠ Q P R$ , $\bar{R Y}$ bisects $∠ S R P$ . Then prove that $R Y P X$ is a parallelogram.

Short Answer

Step by step solution

Step 1. Check the figure.

Step 2. Step description.

Step 3. Step description.

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Given that ▱PQRS, where PX¯bisects ∠QPR, RY¯bisects ∠SRP. Then prove thatRYPXis a parallelogram.

Short Answer

Step by step solution

Step 1. Check the figure.

Step 2. Step description.

Step 3. Step description.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

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Study anywhere. Anytime. Across all devices.

Given that $▱ P Q R S$ , where $\bar{P X}$ bisects $∠ Q P R$ , $\bar{R Y}$ bisects $∠ S R P$ . Then prove that $R Y P X$ is a parallelogram.