Chapter 5: Q28 (page 193)

Given $▱ A Z B Y; \bar{Z Y} ≅ \bar{B X}; ∠ 1 ≅ ∠ 2$ . Prove $A Z B Y$ is a rhombus.

Short Answer

Expert verified

Therefore, AZBY is a rhombus.

Step by step solution

Step 1. Check the figure.

Consider the figure.

Step 2. Step description.

The CPCTC theorem states that when two triangles are congruent, then every corresponding part of one triangle is congruent to the other.

Step 3. Step description.

Consider that $\bar{Z Y} ≅ \bar{B X}; ∠ 1 ≅ ∠ 2$ .

Since the vertical angles are congruent thus $∠ A X B ≅ ∠ Y X Z$ .

By the angle-angle-side postulate $Δ A X B ≅ Δ Y X Z$ .

By the CPCTC theorem, this implies that $A X ≅ X Z; B X ≅ X Y$ .

Therefore, $∠ Y A B$ is a right angle by the definition of a parallelogram.

From the figure, $\bar{A Z}$ is perpendicular bisector to $\bar{B Y}$ and by the definition of rhombus, $\bar{B Y}$ is perpendicular bisector to $\bar{A Z}$ .

Therefore, ABZY is a rhombus.

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Given $▱ A Z B Y; \bar{Z Y} ≅ \bar{B X}; ∠ 1 ≅ ∠ 2$ . Prove $A Z B Y$ 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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Given ▱AZBY;ZY¯≅BX¯;∠1≅∠2. Prove AZBYis 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

Mechanics Maths

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Applied Mathematics

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Study anywhere. Anytime. Across all devices.

Given $▱ A Z B Y; \bar{Z Y} ≅ \bar{B X}; ∠ 1 ≅ ∠ 2$ . Prove $A Z B Y$ is a rhombus.