Q1. - Geometry

Question

Draw, if possible, a triangle in which the perpendicular bisectors of the sides intersect in a point with the location described.

1. A point inside the triangle 
2. A point outside the triangle
3. A point on the triangle

Step-by-Step Solution

Answer

The final answer is:

Step 1. Given information:

   Perpendicular bisectors of triangle located inside, outside, and on the triangle.

Step 2. Concept used:

 We use basic geometric and angle concept.                                  

Step 3. Applying the concept:

Draw an equilateral or an acute triangle ABC.

From three sides of the triangle, draw three perpendicular bisectors.

Thus, all the perpendicular bisectors meet at a point inside the triangle as shown below:

The final answer is:

Step 1. Given information:

   Perpendicular bisectors of triangle located inside, outside, and on the triangle.

Step 2. Concept used:

 We use basic geometric and angle concept.                                  

Step 3. Applying the concept:

Draw an obtuse triangle (one of the angles is greater than 90 degrees.)

From three sides of the triangle, draw three perpendicular bisectors.

Thus, all the perpendicular bisectors meet at a point outside the triangle as shown below:

The final answer is:

Step 1. Given information:

   Perpendicular bisectors of triangle located inside, outside, and on the triangle.

Step 2. Concept used:

 We use basic geometric and angle concept.                                  

Step 3. Applying the concept:

Draw a Right-angled triangle (one of the angles is of 90 degrees.)

From three sides of the triangle, draw three perpendicular bisectors.

Thus, all the perpendicular bisectors meet at a point on the triangle. In fact, they meet at a point which lies on the hypotenuse as shown below: