This is the true statement ΔABC≅ΔXYZ due to SAS, ASA, and LA, which are correct options (A) SAS, (B) ASA, and (D) LA
What are congruent triangles?
Two triangles are said to be congruent if their corresponding sides and angles are equal.
In ΔABC and ΔXYZ,
Side BC = Side YZ
∠C = ∠Z = 90°
Side AC = Side XZ
According to SAS, two triangles are congruent if the two sides and the included angle of one triangle are equal to the corresponding sides and the included angle of the other triangle.
In ΔABC and ΔXYZ,
∠A = ∠X
Side AC = Side XZ
∠C = ∠Z
According to ASA, two triangles are congruent if any two angles and the side included between them of one triangle are equal to the corresponding angles and the included side of the other triangle.
AB = XY is not given. The Pythagorean Theorem can be used to determine that they are equivalent, however, Side-Side-Side cannot be used because it is not a given.
In ΔABC and ΔXYZ,
AC = XZ
∠A = ∠X
Legs and acute Angles are congruent
Hence, ΔADB ≅ ΔBDC due to SAS, ASA, and LA
Learn more about congruent triangles here:
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