Question

1. essential question what are the properties of the perpendicular bisectors in a triangle? what are the properties of the angle bisectors in a triangle?

Explanation:

• Perpendicular bisectors:
• A perpendicular bisector of a side of a triangle is a line that is perpendicular to the side and passes through its mid - point.
• The three perpendicular bisectors of a triangle intersect at a single point called the circum - center.
• The circum - center is equidistant from the three vertices of the triangle. It is the center of the circum - circle (the circle passing through the three vertices of the triangle).
• Angle bisectors:
• An angle bisector of an angle of a triangle is a line that divides the angle into two equal parts.
• The three angle bisectors of a triangle intersect at a single point called the in - center.
• The in - center is equidistant from the three sides of the triangle. It is the center of the in - circle (the circle tangent to the three sides of the triangle).

Answer:

• Perpendicular bisectors: Intersect at circum - center (equidistant from vertices, center of circum - circle).
• Angle bisectors: Intersect at in - center (equidistant from sides, center of in - circle).