Chapter 5: Q3 (page 179)

M, N and T are the midpoints of the sides of $Δ XYZ$ .
If $TN = 7$ , then $XY = \underline{?}$

Short Answer

Expert verified

The length of XY is 14 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 $T N = 7$ .

Step 2. Show the calculation.

Consider in triangles TXM 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 TM 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 YZX are the corresponding angles. Hence, line NM and ZX or ZT are parallel to each other.

Thus, MNZT is parallelogram.

Similarly, TNXM is a parallelogram.

$T N = X M$ .

The side XY is calculated as follows:

$\begin{matrix} T N = X M \\ 7 = \frac{X Y}{2} \\ X Y = 14 units \end{matrix}$

Step 3. State the conclusion.

Therefore, the length of XY is 14 units.

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M, N and T are the midpoints of the sides of $Δ XYZ$ .
If $TN = 7$ , then $XY = \underline{?}$

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 TN=7, thenXY=?¯

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

Calculus

Probability and Statistics

Mechanics Maths

Statistics

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Pure Maths

Study anywhere. Anytime. Across all devices.

M, N and T are the midpoints of the sides of $Δ XYZ$ .
If $TN = 7$ , then $XY = \underline{?}$