Explain Side-Side-Angle Potential Congruency Rule for Triangles

Question

Explain why Side-Side-Angle is not one of the congruence rules for triangles and the conditions under which it does guarantee congruence, including Hypotenuse-Side

Answer 1

Answer 2

SSA or Side Side Angle CANNOT be used to prove triangles congruent at all times as it allows for the possibility of triangles of various shapes and sizes.

For example: One triangle with a side side and angle not included between the two sides is congruent to the other triangle it may work and we are all set. But we can draw the second triangle again. Since the angle is not included (not in between the two sides) we can change the size of the side and not change the original angle at all. But if we change the side the triangles are different and we no longer have congruence.

In summary: you cannot use it on its own to prove congruence but with another rule you may. It CAN work but it does NOT always work.

If

There are six factors that show congruence when it comes to triangles.

If you have a Triangle ABC and Triangle DEF

The follow are true:

SIDES are congruent

AB = DE

BC = EF

CA = FD

ANGLES are congruent

<A = <D

<B = <E

<C =<F

Luckily when asked for congruence you do not have to use ALL 6 truths. You can use other combinations and facts:

SSS = Side Side Side

Three sides of one triangle are congruent to the other sides of the other triangle

ASA = Angle Side Angle

If two angles and the included side of one triangle are congruent to the other triangle then both triangles are congruent.

SAS - Side Angle Side

If two sides and an included angle (between the two sides) of one triangle are congruent to the corresponding parts of another triangle then both triangles are congruent

AAS - Angle Angle Side

If two angles and the NON-included side (not in between the two angles) of one triangle is congruent to the other triangle then both triangles are congruent.

HL - Hypotenuse - Leg

If the hypotenuse and leg of one RIGHT triangle are congruent with the other right triangle then the triangles are congruent

Congruence is usually drawn on the triangles. A line is used on sides and an arc for angles. If side AC has two lines and side DF has two lines it is tell you that side AC and DF are congruent.