Q2. - Geometry

Question

These exploratory exercises can be done using a computer with a program that draws and measures geometric figures.

2. a. Draw  any acute $▵ABC.$Draw the perpendicular  bisector of each side of the triangle. They should intersect in one point. Measure the distance from this point of intersection to each of the vertices of the triangle. What do you notice?

b. repeat using an obtuse triangle and a right triangle. Is the same result true for these triangles as well?

c. In a right triangle, the perpendicular bisectors of the sides intersect in what point?                                                                  

Step-by-Step Solution

Answer

The final answer is:

Step 1. Given information:

 Triangle have angle bisectors and perpendicular segments to each side.    

Step 2. Concept used:

 We use basic geometric and angle concept.                                  

Step 3. Applying the concept:

The perpendiculars are equal in measurement. 

The final answer is:

Step 1. Given information:

 Triangle have angle bisectors and perpendicular segments to each side.    

Step 2. Concept used:

 We use basic geometric and angle concept.                                  

Step 3. Applying the concept:

Obtuse angled triangle right triangle.

In obtuse angled triangle the perpendiculars are not equal in measurement and in right angle triangle all perpendicular are equal.

The final answer is perpendicular bisectors of right triangle intersect at the vertex of the triangle.

Step 1. Given information:

 Triangle is right angle.    

Step 2. Concept used:

 We use basic geometric and angle concept.                                  

Step 3. Applying the concept:

As the triangle’s edges are perpendicular to each other, its perpendicular bisectors will also intersect at the corner where the right angle is located.