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Chapter 2: Q18 (page 47)

Mention what can be deduced from the given information.

Given: AC炉bisects DB炉

DB炉bisects AC炉

CE=BE

Short Answer

Expert verified

The information that can be deduced is:

AC=BDandAE=CE=BE=DE

Step by step solution

01

Step 1. Observe the diagram.

Here, AC炉bisect DB炉, DB炉bisects AC炉and CE=BE.

02

Step 2. Show the calculation.

It is known that AE=CEbecause the segment is bisected.

Then due tthe same reason BE=DE.

But, because CE=BE, all of them are equal (transitive property).

Now AC=BDbecause each is made up of two of the smaller segments, which are all equal.

Thus, AC=BD

AE=CE=BE=DE

03

Step 3. State the conclusion.

Therefore, the information that can be deduced considering the diagram and the information AC炉 bisect DB炉, DB炉bisects AC炉and CE=BEare:

AC=BDand

AE=CE=BE=DE

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