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Chapter 5: Q8 (page 179)

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

State how many parallelograms are in the diagram.

Short Answer

Expert verified

There are 3 parallelograms in the diagram.

Step by step solution

01

Step 1. Consider the diagram.

螖XYZis:

Here, M, N and T are midpoints of 螖XYZ.

02

Step 2. Show the calculation.

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

Thus, MNZT is parallelogram.

Similarly, TNXM is also a parallelogram.

Similarly, TNMY is also a parallelogram

03

Step 3. State the conclusion.

Therefore, the total number of parallelograms is 3.

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Most popular questions from this chapter

Quadrilateral ABCD is a parallelogram. Name the principal theorem or definition that justifies the statement.

AD炉鈮�BC炉

Write a paragraph proof.

Given: 鈻�ABCD;鈥夆赌�鈻�BEDF

Prove: AECF is a 鈻�.

(Hint: A short proof is possible if certain auxiliary segments ate drawn.)

The coordinates of three vertices of parallelogram ABCD are given. Plot the points and find the coordinates of the fourth vertex.

A(3,2),B(8,2),C(?,?),D(0,5)

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

If ZN=8, then TM=?炉

鈻�DECKis a parallelogram. Complete.

If m鈭�1=42,m鈭�2=x2and m鈭�CED=13xthen m鈭�2=?or m鈭�2=?(numerical answers).
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