Constructing an Inscribed Circle on a Triangle Using Angle Bisectors

This lesson teaches how to construct an inscribed circle within a triangle using angle bisectors. It explains the concept of angle bisectors, triangle centers, and the Euler line. The inscribed circle is defined as the largest circle within a triangle, tangent to its sides. The construction process involves drawing a triangle, finding angle bisectors, and using them to locate the circle's center. The radius is determined by drawing a perpendicular from the center to a triangle side. The lesson concludes with using a compass to draw the inscribed circle.

What is an angle bisector?

• A line that divides a triangle into two equal areas

• A ray that divides an angle into two equal parts

• A segment that connects the midpoints of two sides of a triangle

• A line that is perpendicular to one side of a triangle

Which of the following is true about the centers of a triangle?

• The center of a triangle is always at its centroid

• All triangles have only one center

• The centers of a triangle always lie on the Euler line

• Triangles have multiple centers that create relationships within the triangle

Where is the center of an inscribed circle located?

• At the intersection of the triangle's angle bisectors

• At the centroid of the triangle

• At the intersection of the triangle's medians

• At the midpoint of the triangle's longest side

What is the first step in constructing an inscribed circle?

• Find the centroid of the triangle

• Draw a circle around the triangle

• Measure the angles of the triangle

• Draw a triangle

How do you determine the radius of an inscribed circle?

• By measuring the longest side of the triangle

• By drawing a perpendicular line from the center to any side of the triangle

• By finding the midpoint of the triangle's base

• By calculating the average of the triangle's angles