Hl & ha
The HA and HL theorems for right triangles or the Pythagorean theorem might be of use.
Not necessarily. Even if all three angles of one triangle are the same as the corresponding angles of the other, the triangles may be similar but not congruent. And in this case, you don't even know that all three angles are the same.
No, because the third-angle theorem requires that you know two angles of each of the triangles. Assuming ASS, you only know one angle. In fact, two triangles may have the same ASS and not be congruent. See if you can make two non-congruent triangles with Angle 60 deg, Side 10, and Side 9.
Free Math Study GroupCongruent TrianglesDefinition: Triangles are congruent when all corresponding sides and interior angles arecongruent. The triangles will have the same shape and size, but one may be a mirror image of the other.In the simple case below, the two triangles PQR and LMN are congruent because every corresponding side has the same length, and every corresponding angle has the same measure. The angle at P has the same measure (in degrees) as the angle at L, the side PQ is the same length as the side LM etc.Try this Drag any orange dot at P,Q,R. The other triangle LMN will change to remain congruent to it.(If there is no image below, see support page.)
No, they are similar. They may be congruent, but they need not be.
No. Angles are not congruent. (Triangles may be congruent.)
Two triangles with three congruent angles may have different side lengths.
congruent
Hl & ha
The HA and HL theorems for right triangles or the Pythagorean theorem might be of use.
They may not be. Depends on the triangles! All the angles and sides have to be the same to be congruent. They would be identical. The same angles but proportionally larger or smaller side lengths = similar.
Not necessarily. Even if all three angles of one triangle are the same as the corresponding angles of the other, the triangles may be similar but not congruent. And in this case, you don't even know that all three angles are the same.
No, because the third-angle theorem requires that you know two angles of each of the triangles. Assuming ASS, you only know one angle. In fact, two triangles may have the same ASS and not be congruent. See if you can make two non-congruent triangles with Angle 60 deg, Side 10, and Side 9.
Free Math Study GroupCongruent TrianglesDefinition: Triangles are congruent when all corresponding sides and interior angles arecongruent. The triangles will have the same shape and size, but one may be a mirror image of the other.In the simple case below, the two triangles PQR and LMN are congruent because every corresponding side has the same length, and every corresponding angle has the same measure. The angle at P has the same measure (in degrees) as the angle at L, the side PQ is the same length as the side LM etc.Try this Drag any orange dot at P,Q,R. The other triangle LMN will change to remain congruent to it.(If there is no image below, see support page.)
Just because they look the same does not mean they are. Normally if sides are congruent they are marked by the same indicator. Which is usually a line, number, or letter. Same thing with angles, except angles would not use lines to indicate congruency. If you have any three congruent parts on triangles (the number may change due the shape) then those triangles are congruent.
You make a dimondxoxoxoxoxoxoxoxo