Chapter 5: Q7 (page 179)

M, N and T are the midpoints of the sides of $Δ XYZ$ .
State the theorem suggested by Exercise 6.

Short Answer

Expert verified

The theorem stated by Exercise 6 is the Midpoint Theorem.

Step by step solution

Step 1. Consider the diagram.

$Δ X Y Z$ is:

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

Step 2. State the explanation.

Midpoint Theorem:

If the line joining midpoints of any triangle is parallel to the third side of that triangle, then this line is equal to the half of the third side of the triangle.

Now in $Δ X Y Z$ ,

Since T and N are the midpoints of ZX and ZY respectively.

So, according to Midpoint Theorem,

TN is parallel to XY and $T N = \frac{1}{2} X Y$ .

Since N and M are the midpoints of ZY and YX respectively.

So, according to Midpoint Theorem,

NM is parallel to ZX and $N M = \frac{1}{2} Z X$ .

Since M and T are the midpoints of YX and XZ respectively.

So, according to Midpoint Theorem,

MT is parallel to YZ and $M T = \frac{1}{2} Y Z$ .

Step 3. State the conclusion.

Therefore, the theorem stated by Exercise 6 is the Midpoint Theorem.

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M, N and T are the midpoints of the sides of $Δ XYZ$ .
State the theorem suggested by Exercise 6.

Short Answer

Step by step solution

Step 1. Consider the diagram.

Step 2. State the explanation.

Step 3. State the conclusion.

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M, N and T are the midpoints of the sides of ΔXYZ.State the theorem suggested by Exercise 6.

Short Answer

Step by step solution

Step 1. Consider the diagram.

Step 2. State the explanation.

Step 3. State the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Discrete Mathematics

Theoretical and Mathematical Physics

Applied Mathematics

Decision Maths

Calculus

Study anywhere. Anytime. Across all devices.

M, N and T are the midpoints of the sides of $Δ XYZ$ .
State the theorem suggested by Exercise 6.