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Chapter 5: Q4 (page 179)

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

If ZN=8, then TM=?炉

Short Answer

Expert verified

The length of TM is 8 units.

Step by step solution

01

Step 1. Consider the diagram.

螖XYZis:

Here, M, N and T are midpoints of 螖XYZ. And ZN=8.

02

Step 2. Show the calculation.

Consider in triangles TXN and ZXY .

鈭�TXM=鈭�ZXY (Common).

TXZX=XMXY=12 (Midpoints).

Therefore, 螖TXM~螖ZXY(SAS).

鈭�XMT=鈭�XYZ鈭�MTX=鈭�YZX

Angle XMT and XYZ are the corresponding angles. Hence, line TN and ZY or ZN are parallel to each other.

Consider in triangles NMY and ZXY .

鈭�NYM=鈭�ZYX (Common).

NYZY=YMYX=12 (Midpoints).

Therefore, 螖NMY~螖ZXY(SAS).

鈭�YNM=鈭�YZX鈭�YMN=鈭�YXZ

Angle YNM and YZK are the corresponding angles. Hence, line NM and ZX or ZT are parallel to each other.

Thus, MNZT is parallelogram.

TM=ZN.

The side TN is calculated as follows:

TM=ZNTM=8units

03

Step 3. State the conclusion.

Therefore, the length of TM is 8 units.

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