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Chapter 5: Q7 (page 182)

Given that 鈻�ABCD and M is the midpoint of AB炉. Then prove that MO=12AD.

Short Answer

Expert verified

The statement is MO=12AD.

Step by step solution

01

Step 1. Check the figure.

Consider the figure.

02

Step 2. Step description.

Consider that the two triangles 螖MOB,螖ADB.

Here 鈭�Bis common in both the angles such that 鈭�MBO=鈭�ABD.

Since M is the midpoint of AB such that MBAB=12.

From the figure, the diagonals of the parallelogram intersect each other as OBDB=12.

03

Step 3. Step description.

By the SAS postulates, it is clear that 螖MOB~螖ADB.

Since MOAD=12thus MO=12AD

Therefore, MO=12AD.

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Most popular questions from this chapter

Given: ABCDis a 鈻�,鈭�A鈮�鈭�E

Prove: localid="1637661691185" AB炉鈮�CE炉

Study the markings on each figure and decide whether ABCD must be a parallelogram. If the answer is yes, state the definition or theorem that applies.

Study the markings on each figure and decide whether ABCD must be a parallelogram. If the answer is yes, state the definition or theorem that applies.

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

If XZ=10, then MN=?炉

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

鈭�ADX鈮�鈭�CBX
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