Question

which triangle congruence theorem could be used to show angle 1 is congruent to angle 2

SSS
SAS
ASA
AAS

PICTURE 2 question
which angle do EBC and ADC share?
EDF
ECA
CAF
ADC

PICTURE 3 question
what common side does ABC share with ADC
BC
AD
BD
AC

Answer 1

Heya User,

For (1) --->

SAS 'coz two sides are equal and Vertically opposite angles are equal and b/w the Arms.......

For (2) --- > 
The common Angle is ECA

For (3) ---->
As the name suggests, the common side is AC ☺

Answer 2

Answer: The correct options are (B) SAS, (B) ∠ECA and (D) AC.

Step-by-step explanation:  The explanations are given one by one as follows:

(1) Since ∠1 and ∠2 are vertically opposite angles, so they must be equal.

Therefore, in both the triangles, two pairs of corresponding sides and the angle included between them are congruent.

Therefore, we can use SAS (side-angle-side) congruence theorem.

Thus, (B) SAS is the correct option.

(2) We can see that in ΔEBC and ΔADC, ∠ECA is common in both the triangles.

Therefore, the two triangles share ∠ECA.

Thus, (B) ∠ECA is the correct option.

(3) We can see that in ΔABC and ΔADC, AC is the side which is common to both the triangles.

Therefore, ΔABC shares the side AC with ΔADC.

Thus, (D) AC is the correct option.