Question

Given: B bisects EA, FE is parallel to CA, DC is parallel

to GF
Prove: Triangle BGF Triangle BDC
Which method?
E
SSS
SAS
AAS
С
OHL
וד
B
ASA
A
INTL 9:53

Answer 1

To prove that triangle BGF is congruent to triangle BDC, we can use the angle-angle-side (AAS) congruence criterion by showing that they have the same size and shape.

Step-by-step explanation:

To prove that triangle BGF is congruent to triangle BDC, we need to show that they have the same size and shape. We can do this by using the angle-angle-side (AAS) congruence criterion. In order to apply AAS, we need to prove that angle BGF is congruent to angle BDC, angle BFG is congruent to angle BCD, and side BG is congruent to side BD.

Since B is the midpoint of EA, we can conclude that triangle BGF is congruent to triangle BDC using the fact that corresponding parts of congruent triangles are congruent (CPCTC).

Answer 2

Choice 3: AAS

Step-by-step explanation:

We can prove that by AAS that means we need two congruent angles and one congruent side.

The first angle will be the vertical pair <FBG and <DBC.

The second angle will be the alternate interior pair <G and <D.

The one side will be
`\overline{GB}` and
`\overline{BD}`.