You can construct triangles if you know which of the following.
select two answers
a. the measure of three angles
b.the measure of one side and one angle
c.the measure of two angles
d.the measure of two angles and one given side
e.the measure of two sides and the include angle
E for sure
a and c are really the same, and neither will work
so, what do you think is the other correct choice?
To construct triangles, you need to know certain combinations of measurements. Here are the possible options:
a. The measure of three angles: If you know the measures of all three angles of a triangle, you can construct the triangle. However, keep in mind that the angle measurements must satisfy the triangle inequality theorem, which states that the sum of any two angles of a triangle must be greater than the measure of the third angle.
b. The measure of one side and one angle: This combination is also sufficient to construct a triangle. If you know the length of one side and the measure of one angle (which is not the included angle), you can draw the side to scale and then use the given angle to determine the position of the other two sides.
c. The measure of two angles: If you know the measures of two angles in a triangle, you can calculate the third angle (as the sum of angles in a triangle is always 180 degrees). With this information, you can construct the triangle.
d. The measure of two angles and one given side: This combination is enough to construct a triangle. The given side can be drawn to scale, and the two angles can be placed on either end of the side. Then, the remaining two sides can be drawn using the angle-side-angle (ASA) congruence criterion.
e. The measure of two sides and the included angle: If you know the measures of two sides of a triangle and the included angle (the angle formed by the two given sides), you can construct the triangle using the side-angle-side (SAS) congruence criterion. Draw one of the given sides to scale, then use the included angle to position the other side accordingly.
In summary, you can construct triangles if you know:
- The measure of three angles
- The measure of one side and one angle
- The measure of two angles
- The measure of two angles and one given side
- The measure of two sides and the included angle.