Draw any triangle and fix the length of two of its sides and the measure of the smallest of the non-included angles. Draw the line containing the third side and consider a point on it such that its distance to the vertex not on the line equals the length of the side opposite to the fixed angle.
See solution.
Practice makes perfect
Let's consider the two triangles below.
Next, we list the corresponding congruent parts.
cc
BC ≅ QR & Side
CA ≅ RP & Side
∠A ≅ ∠P & Non-included Angle
Despite the congruent parts between both triangles, they are not congruent. We can verify it by finding the remaining two angles of each triangle.
Since two angles of â–³ ABC are not congruent to the angles of â–³ PRQ, then these pair of triangles cannot be congruent. This is why Side-Side-Angle (SSA)cannot be used to prove the congruence of two triangles.
Extra
Building the Triangles
To find the triangles used before, we begin by drawing any triangle. Let's draw â–³ ABC for example.
Next, we draw the line containing AB and rotate BC around C until the endpoint lies on AB.
As we can see, after rotating BC, we obtained the second triangle we used before.
