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Chapter 5: Q28 (page 193)

Given 鈻�AZBY;ZY炉鈮�BX炉;鈭�1鈮�鈭�2. Prove AZBYis a rhombus.

Short Answer

Expert verified

Therefore, AZBY is a rhombus.

Step by step solution

01

Step 1. Check the figure.

Consider the figure.

02

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.

03

Step 3. Step description.

Consider that ZY炉鈮�BX炉;鈭�1鈮�鈭�2.

Since the vertical angles are congruent thus 鈭�AXB鈮�鈭�YXZ.

By the angle-angle-side postulate 螖AXB鈮�螖YXZ.

By the CPCTC theorem, this implies that AX鈮�XZ;BX鈮�XY.

Therefore, 鈭�YABis a right angle by the definition of a parallelogram.

From the figure, AZ炉is perpendicular bisector to BY炉and by the definition of rhombus, BY炉is perpendicular bisector to AZ炉.

Therefore, ABZY is a rhombus.

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