Q14. - Geometry

Question

a.  Draw an acute triangle. Construct the perpendicular bisector of each side.

b. Do the perpendicular bisectors intersect in one point?

c. Repeat  pairs (a) and (b) using an obtuse triangle.

Step-by-Step Solution

Answer

a. The final answer is $5\sqrt{5}.$

b. The final answer is $5\sqrt{5}.$

Part a. Step 1. Given information:

An acute triangle.

Step 2. Concept used:

 We use basic geometric and angle concept.                                  

Step 3. Applying the concept

An acute is in which all interior angles are less than$90°$ is drawn below.

First, draw perpendicular bisector of side $AB$ using following steps.

1. Using $C$as centre, draw two arcs of equal radii that intersect $AB$ at $X$ and $Y$.
2. Using $X$ and $Y$ as centres and a suitable radius, draw arcs that intersect at point $Z$.
3. Join $CZ$, it is a perpendicular bisector of side $AB$ as shown below.

Similarly, perpendicular bisector side $BC$ and $AC$ are drawn as shown below.

 (b). Perpendicular bisectors are shown below:

Yes, they do intersect at a point.

Part b. Step 1. Given information:

An obtuse triangle.

Step 2. Concept used:

 We use basic geometric and angle concept.                                  

Step 3. Applying the concept

$90°$An obtuse  is in which all interior angles are greater than\[{{90}^{\circ }}\] is drawn below.

First, draw perpendicular bisector of side $AB$ using following steps.

1. Using $C$as centre, draw two arcs of equal radii that intersect $AB$ at $X$ and $Y$.
2. Using $X$ and $Y$ as centres and a suitable radius, draw arcs that intersect at point $Z$.
3. Join $CZ$, it is a perpendicular bisector of side $AB$ as shown below.

Similarly, perpendicular bisector side $BC$ and $AC$ are drawn as shown below.