Answer:
5. AAS (Angle-Angle-Side) axiom
6. ASA (Angle-Side-Angle) axiom
Explanation:
Note:
There are four basic conditions under which two triangles are congruent. These are:
- SSS (Side-Side-Side): If all three pairs of corresponding sides of two triangles are equal, then the triangles are congruent.
- SAS (Side-Angle-Side): If two pairs of corresponding sides of two triangles are equal, and the angles between those sides are also equal, then the triangles are congruent.
- ASA (Angle-Side-Angle): If two pairs of corresponding angles of two triangles are equal, and the sides between those angles are also equal, then the triangles are congruent.
- AAS (Angle-Angle-Side): If two pairs of corresponding angles of two triangles are equal, and the side that includes one of those angles is also equal, then the triangles are congruent.
One of the conditions should be needed to fulfill to determine whether the two triangles are congruent.
Over here:
5.
In ΔABC and ΔBCD
∡BAC= ∡BDC Given Angle
∡BCA=∡CBD Given Angle
BC=BC Same side Side
It fulfills the condition of the AAS (Angle-Angle-Side) axiom.
ΔABC ≅ ΔBCD by AAS (Angle-Angle-Side) axiom.
6.
In ΔVOL and ΔVOE
∡LOV= ∡EOV Given Angle
VO=VO Same side Side
∡LVO=∡OVE Given Angle
It fulfills the condition of the ASA (Angle-Side-Angle)axiom.
ΔVOL≅ ΔVOE by the ASA (Angle-Side-Angle) axiom.