If ΔDEF ≅ ΔBCA, write the part(s) of ΔBCA that correspond to
(i) ∠E (ii) EF (iii) ∠F (iv) DF
Answers
Step-by-step explanation:
(i) ∠C
(ii) CA
(iii) ∠A
(iv) BA
(i) ∠E ↔ ∠C
(ii) side EF ↔ side CA
(iii) ∠F ↔ ∠A
(iv) side DF ↔ side BA
Step-by-step explanation:
Given:
ΔDEF ≅ ΔBCA
To find:
the corresponding angles and sides to the triangle BCA
Solution:
It is given that ΔDEF ≅ ΔBCA,
Hence, the corresponding angles and corresponding sides will also be congruent.
To find the corresponding angles and sides we look at the names of the triangles DEF & BCA
⇒ The angle E is positioned 2nd in the name DEF, hence its corresponding angle will be the second angle positioned in the name BCA
∴ ∠E ≅ ∠C
So, ∠E ↔ ∠C
⇒ side EF has the vertices E & F positioned second and third respectively in the name of the triangle DEF
Hence, the second and third vertices of ΔBCA are C & A respectively
The side formed will be CA
∴side EF ≅ side CA
side EF ↔ side CA
⇒ Now the angle F will correspond to the third angle of the ΔBCA because it is at the third position in the name DEF
∴ ∠F≅∠A
∠F ↔ ∠A
⇒ side DF will correspond to side BA as the position of the vertices in the name of the triangles is taken into consideration.
∴ side DF≅ side BA
side DF ↔ side BA