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Chapter 5: Q2 (page 180)

Points A, B, E and F are midpoints of XC炉,XD炉,YC炉and YD炉. Complete.

If AB=k, then CD=? and EF=? .

Short Answer

Expert verified

CD=2k and EF=k .

Step by step solution

01

Step 1. Consider the diagram.

Here, A, B, E and F are the midpoints of sides XC炉,XD炉,YC炉and YD炉 respectively.

and AB=k

02

Step 2. Show the calculation.

Consider the triangle 鈻�XCD.

Here, points A and B are the midpoints of XC炉and XD炉.

So, by theorem 5-11 part (2), the side AB炉 is half as long as the third side CD炉.

AB=12CD

So,

CD=2AB=2k

Consider the triangle 鈻�YCD.

Here, points E and F are the midpoints of YC炉and YD炉.

So, by theorem 5-11 part (2), the side EF炉is half as long as the third side CD炉.

EF=12CD=12脳2k=k

03

Step 3. State the conclusion.

Therefore, CD炉=2k and EF炉=k.

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