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Chapter 5: Q29 (page 193)

Given 鈻�AZBY;AY炉鈮�BX炉. Prove 鈭�1鈮�鈭�2,;鈭�1鈮�鈭�3.

Short Answer

Expert verified

鈭�1鈮�鈭�2,;鈭�1鈮�鈭�3

Step by step solution

01

Step 1. Check the figure.

Consider the figure.

02

Step 2. Step description.

The opposite sides of the rhombus are parallel am transversal.

03

Step 3. Step description.

From the figure, ZY炉鈮�BX炉.

From the triangles 螖AYZand 螖ABZ,

Sides of rhombus are equal thus, ZB=AB.

Since the angles opposite to equal sides are equal thus 鈭�1鈮�鈭�3 鈥�... (1)

Since the opposite sides of a rhombus are parallel and transversal AZthus AY鈭�BZ.

As the alternate angles are congruent thus, 鈭�1鈮�鈭�4 鈥︹�� (2)

Therefore, from the equations (1) and (2) it follows that 鈭�1鈮�鈭�2.

Thus, 鈭�1鈮�鈭�2and 鈭�1鈮�鈭�3.

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Most popular questions from this chapter

Suppose that 鈭�M is a right angle. What can you deduce about angles G, R, and A?

Draw and label a diagram. List what is given and what is to be proved. Then write a two-column proof of the theorem.

Theorem 5-5.

M, N and T are the midpoints of the sides of 螖XYZ.

If XY=k, thenTN=?炉

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