Learn to construct a triangle given two sides and the included angle (SAS) or two angles and the included side (ASA).
Preview · progress not saved — Chapter 1 is free
Define 'included angle' and introduce the SAS construction concept.
We have seen how to construct triangles given all three side lengths. Now, we will explore constructing a triangle when two sides and one angle are known.
This is called the SAS (Side-Angle-Side) method.
Must show angle placement relative to sides.
Notice how the known angle sits between the known sides in SAS, while the known side sits between the known angles in ASA.
Worked steps for constructing AB=5cm, AC=4cm, angle A=45°.
Problem. Construct a triangle with , , and an included angle .
Faded steps to construct a triangle with 3cm, 120°, and 8cm.
To construct a triangle with sides and and an included angle of , we must carefully follow the SAS method. We start by drawing the of the triangle using a ruler. Let's say we draw the segment first as our starting line. Next, we place a protractor at one of the endpoints to measure our angle. We mark a angle, which is an obtuse angle, and draw a long line through it. Finally, we measure exactly along this new angled line to mark our third vertex. Connecting this third vertex to the other end of our starting line completes the construction.
Define 'included side' and introduce ASA construction.
Now, let's look at another common scenario: constructing a triangle when we know two angles and the side between them.
This is known as the ASA (Angle-Side-Angle) method.
Worked steps for constructing AB=5cm, A=45°, B=80°.
Problem. Construct a triangle where the included side , , and .
MCQ testing the limit of two angles summing to >= 180°.
If you are given a base side for an ASA construction, what happens if the two angles you are given are both or greater?