### Edexcel GCSE Maths

Numbers
Algebra
Geometry and Measures
Probability
Statistics

# Constructing Triangles

To construct triangles, you’ll typically need a straightedge (e.g. a ruler), a protractor and a pair of compasses. You can construct triangles using three main criteria:

• Side-Side-Side (SSS)
• Angle-Side-Angle (ASA)
• Side-Angle-Side (SAS)

## Constructing SSS Triangles

An SSS triangle is a triangle in which the lengths of all three sides are known. To construct a triangle when you are given all three sides, follow these steps:

1. Use a ruler and a pencil to draw a line equal to the length of the longest side given, as a horizontal base.

2. Place the compass point on one endpoint of the line and adjust its width to the length of the second side. Draw an arc above or below the line segment.

3. Similarly, place the compass point on the other endpoint of the line and adjust its width to the length of the third side. Draw another arc that intersects the first arc.

4. Draw line segments connecting the intersection point of the arcs to both endpoints of the original line . This completes the construction of the triangle.

5. Use your ruler to verify that the sides match the measurements you were given.

• This is an equilateral triangle

## Constructing SAS Triangles

SAS means side-angle-side, which is when the lengths of two sides and the measure of an angle of the triangle are known. To construct a triangle when you are given the lengths of two sides and one of the angles, follow these steps:

1. Use a ruler and a pencil to draw a line equal to the length of the longest side given, as a horizontal base.

2. Place the centre point of your protractor on one endpoint of the line, measure the given angle and mark a small dot at the appropriate degree mark on the protractor.

3. Remove the protractor and use the ruler to draw a line from the endpoint of the base to the dot marked in step 2. This line forms the given angle with the base.

4. Measure the length of the second side using the ruler and mark that distance along the line you drew in step 3.

5. Draw a line connecting the mark from step 4 to the other endpoint of the original line.

6. Use a ruler and a protractor to make sure that the measurements of the sides and angles of your triangle match the measurements given in the question.

## Constructing ASA Triangles

An ASA triangle is a triangle in which the measures of two angles and the length of the included side are known. To construct an ASA triangle, follow these steps:

1. Use a ruler and a pencil to draw a line equal to the length of the given side.

2. Place the centre point of the protractor on one endpoint of the line segment, use it to measure the first given angle and mark a small dot at the appropriate degree mark on the protractor. Remove the protractor and use the ruler to draw a straight line from the endpoint of the base to the dot marked.

• This line forms the first given angle with the base

3. Repeat step 2 for the second given angle at the other endpoint of the original line.

4. Extend the rays that form the angles until they intersect each other.

• This intersection point will be the third vertex of the triangle