Chapter 5: Q7 (page 195)

Quad WXYZ must be a special figure to meet the conditions stated. Write the best name for that special quadrilateral.
Given that $∠ 1 ≅ ∠ 2 ≅ ∠ 3 ≅ ∠ 4$ . Prove that $E F G H$ is a rhombus.

Short Answer

Expert verified

The parallelogram is a rhombus.

Step by step solution

Step 1. Check the figure.

Consider the figure.

Step 2. Step description.

From the figure, for the lines $\bar{H E}$ and $\bar{G F}$ and the transversal $\bar{E G}$ , the corresponding angles $∠ 1$ and $∠ 3$ are congruent.

So, the lines $\bar{H E}$ and $\bar{G F}$ are parallel.

Similarly, for the lines $\bar{H G}$ and $\bar{E F}$ and the transversal $\bar{E G}$ , the corresponding angles $∠ 2$ and $∠ 4$ are congruent.

So, the lines $\bar{H G}$ and $\bar{E F}$ are parallel.

Consider the quadrilateral $E F G H$ .

It is known that if pairs of opposite sides of any quadrilateral are parallel, then it is a parallelogram.

Step 3. Step description.

Here, $\bar{H E} ∥ \bar{G F}$ and $\bar{H G} ∥ \bar{E F}$ so, $E F G H$ is a parallelogram.

Now, for the triangle $△ E G F$ , $∠ 2 ≅ ∠ 3$ .

So, the sides $\bar{G F}$ and $\bar{E F}$ are congruent.

As $\bar{E F} ≅ \bar{G F}$ , thus the parallelogram $E F G H$ is a rhombus.

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Quad WXYZ must be a special figure to meet the conditions stated. Write the best name for that special quadrilateral.
Given that $∠ 1 ≅ ∠ 2 ≅ ∠ 3 ≅ ∠ 4$ . Prove that $E F G H$ is a rhombus.

Short Answer

Step by step solution

Step 1. Check the figure.

Step 2. Step description.

Step 3. Step description.

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Quad WXYZ must be a special figure to meet the conditions stated. Write the best name for that special quadrilateral.Given that ∠1≅∠2≅∠3≅∠4. Prove that EFGHis a rhombus.

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

Theoretical and Mathematical Physics

Decision Maths

Calculus

Discrete Mathematics

Applied Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

Quad WXYZ must be a special figure to meet the conditions stated. Write the best name for that special quadrilateral.
Given that $∠ 1 ≅ ∠ 2 ≅ ∠ 3 ≅ ∠ 4$ . Prove that $E F G H$ is a rhombus.