answer this maths question please
Answers
Answer:
ΔADC ≅ ΔABC by SAS congruency
Solution:
In ΔADC and ΔABC:
∠CAD = ∠CAB [Given]
AD = AB [Given]
AC = CA [Given]
In ΔADC and ΔABC, two sides and one included angle of one triangle is congruent to another. Hence:
ΔADC ≅ ΔABC by SAS congruency.
Knowledge Bytes:
→ Congruency
We can say that two triangles are congruent to each other if any three basic components of one triangle is equal to the same three basic components of the other triangle. There are four basic congruency rules as discussed below:
✳ SSS congruency [Side-Side-Side Congruency]
In this congruency, the three sides of one triangle is equal to the three sides of the other triangle. That is both the triangles will have sides of equal measures.
✳ SAS congruency [Side-Angle-Side Congruency]
In the congruency rule, the two sides and included angle of one triangle is equal to the two sides and included angle of another triangle.
✳ ASA congruency [Angle-Side-Angle Congruency]
In this congruency rule, the two angles and one included side of one triangle is equal to the two angles and included side of another triangle.
✳ RHS congruency [Right angle-Hypotenuse-Side congruency]
This congruency rule is only applicable for right angled triangles. In two right angled triangles, if the hypotenuse and any one side is equal to the hypotenuse and any one side of the other triangle, they are congruent.