How do you construct a triangle given one angle and two sides?

To construct a triangle given one angle and two sides, use the angle-side-side (ASS) or side-angle-side (SAS) method.

First, identify the given elements: the angle (let's call it \( \angle A \)) and the two sides (let's call them \( b \) and \( c \)). If the given angle is between the two sides, you will use the SAS method. If the angle is not between the two sides, you will use the ASS method.

For the SAS method:
1. Draw one of the given sides, say \( b \), using a ruler.
2. At one end of this side, use a protractor to measure and draw the given angle \( \angle A \).
3. From the vertex of the angle, measure the length of the second side \( c \) along the direction of the angle.
4. Connect the end of this side to the other end of the first side to complete the triangle.

For the ASS method:
1. Draw one of the given sides, say \( b \), using a ruler.
2. At one end of this side, use a protractor to measure and draw the given angle \( \angle A \).
3. From the vertex of the angle, measure the length of the second side \( c \) along the direction of the angle.
4. If the second side does not meet the first side, adjust the angle or side length as necessary to ensure they connect, forming a triangle.

Remember, the ASS method can sometimes result in no triangle or two possible triangles, so always check your measurements carefully.