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Chapter 3: Q5. (page 112)

Complete each statement with the word always, sometimes, or never.

In 鈻�ABC, if AB炉鈯�BC炉, thenAC炉 is?炉 perpendicular to BC炉.

Short Answer

Expert verified

In 鈻�ABC, if AB炉鈯�BC炉, thenAC炉 is never perpendicular to BC炉.

Step by step solution

01

Step 1. Observe the diagram.

The figure is:

02

Step 2. Description of step.

The sum of all the three angles in a triangle is 180掳.

In the triangle ABC, AB炉鈯�BC炉, therefore, the measure of the angle鈭�ABC is 90掳.

Therefore, the triangleABC is a right-angled triangle.

In the right triangle, one of the angles is 90掳, the sum of the other two angles should be equal to 90掳.

Therefore, in the right triangle, not more than one angle can be equal to 90掳.

Therefore, AC炉cannot be perpendicular to BC炉.

03

Step 3. Write the conclusion.

As,AC炉 cannot be perpendicular to BC炉.

Therefore, in 鈻�ABC, if AB炉鈯�BC炉, thenAC炉 is never perpendicular to BC炉.

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