Question

1. what type of information is required to construct a triangle using the sas method?

a. three sides
b. two sides and a non - included angle
c. two sides and the included angle
d. two angles and the included side

1. what is the point called where the perpendicular bisectors of the sides of a triangle meet?

a. centroid
b. orthocenter
c. incenter
d. circumcenter

1. what is required to use the asa method for constructing a triangle in geogebra?

a. the distance between the vertices
b. the length of two sides
c. all angles congruent
d. the measures of two angles

Explanation:

1. In the SAS (Side - Angle - Side) method for constructing a triangle, we need two sides and the included angle. This is a fundamental concept in triangle construction.
2. The point where the perpendicular bisectors of the sides of a triangle meet is called the circumcenter. The circumcenter is equidistant from the vertices of the triangle.
3. For the ASA (Angle - Side - Angle) method of constructing a triangle, we need the measures of two angles and the length of the included side. Among the given options, the most relevant for ASA is the measures of two angles as the side - length information is also crucial but not given as an option alone here and the measures of two angles are a key part of the ASA criteria.

Answer:

1. c. Two sides and the included angle
2. d. Circumcenter
3. d. The measures of two angles