Chapter 5: Q4 (page 179)

M, N and T are the midpoints of the sides of $Δ XYZ$ .
If $ZN = 8$ , then $TM = \underline{?}$

Short Answer

Expert verified

The length of TM is 8 units.

Step by step solution

Step 1. Consider the diagram.

$Δ X Y Z$ is:

Here, M, N and T are midpoints of $Δ X Y Z$ . And $Z N = 8$ .

Step 2. Show the calculation.

Consider in triangles TXN and ZXY .

$∠ T X M = ∠ Z X Y$ (Common).

$\frac{T X}{Z X} = \frac{X M}{X Y} = \frac{1}{2}$ (Midpoints).

Therefore, $Δ T X M ~ Δ Z X Y$ (SAS).

$\begin{array}{l} ∠ X M T = ∠ X Y Z \\ ∠ M T X = ∠ Y Z X \end{array}$

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 .

$∠ N Y M = ∠ Z Y X$ (Common).

$\frac{N Y}{Z Y} = \frac{Y M}{Y X} = \frac{1}{2}$ (Midpoints).

Therefore, $Δ N M Y ~ Δ Z X Y$ (SAS).

$\begin{array}{l} ∠ Y N M = ∠ Y Z X \\ ∠ Y M N = ∠ Y X Z \end{array}$

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

Thus, MNZT is parallelogram.

$T M = Z N$ .

The side TN is calculated as follows:

$\begin{matrix} T M = Z N \\ T M = 8 units \end{matrix}$

Step 3. State the conclusion.

Therefore, the length of TM is 8 units.

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M, N and T are the midpoints of the sides of $Δ XYZ$ .
If $ZN = 8$ , then $TM = \underline{?}$

Short Answer

Step by step solution

Step 1. Consider the diagram.

Step 2. Show the calculation.

Step 3. State the conclusion.

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M, N and T are the midpoints of the sides of ΔXYZ.If ZN=8, then TM=?¯

Short Answer

Step by step solution

Step 1. Consider the diagram.

Step 2. Show the calculation.

Step 3. State the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Statistics

Discrete Mathematics

Theoretical and Mathematical Physics

Mechanics Maths

Calculus

Study anywhere. Anytime. Across all devices.

M, N and T are the midpoints of the sides of $Δ XYZ$ .
If $ZN = 8$ , then $TM = \underline{?}$