Which Triangles are congruent by ASA

Triangles congruent by ASA have two pairs of congruent sides and an included congruent angle.

The graph indicates that sides TV, HG, and AB are congruent, and that sides TU, FG, and BC are congruent. It also indicates that angles U, F, and C are congruent, and that angles G and B are congruent. Notice that angle U of triangle TUV is not an included angle; this eliminates triangle TUV as it can't be congruent to another triangle by ASA with the information provided.

That leaves triangles FGH and ABC. Evidently, angles G and B are included angles, so these triangles are congruent by ASA.

Answer:
b. ΔHGF and ΔABC

lublana lublana · Answer 2 · 2019-12-19T04:54:42+01:00

Answer:

b.[tex]\triangle HGF\cong \triangle ABC[/tex]

Step-by-step explanation:

We are given that three triangles VTU,HGF and ABC.

We have to find the triangle which are congruent by ASA.

ASA postulate: When two angles of one triangle and side on which two equal angles are made are congruent to its corresponding two angles and corresponding side of other triangle then, two triangles are congruent by ASA.

From given figure, we can see that

AB=HG=VT

BC=FG=TU

[tex]\angle V=\angle F=\angle C[/tex]

[tex]\angle G=\angle B[/tex]

Therefore, [tex]\triangle HGF\cong \triangle ABC[/tex]

By ASA postulate because two angle of triangle HGF angle F and angle G and one side FG are congruent to corresponding angles C and B and corresponding side BC.

Option b is true.