Question

Please answer the full question and make sure to specify which triangle is equal to triangle AMN and by which of the following reasons:

AAA
SAA
SSS
Can not be determined

Answer 1

See Below.

Explanation:

Statements: Reasons:

`1)\text{ } \overline{MN} \parallel \overline{AO}\text{ and } \overline{AM} \parallel \overline{ON}` Given

`2)\text{ } AMNO\text{ is a parallelogram}` Definition of a parallelogram

`3)\text{ } \overline{AM}\cong\overline{ NO}` Opposite sides of a parallelogram are ≅.

`4)\text{ } \overline{MN }\cong\overline{ OA}` Opposites sides of a parallelogram are ≅.

`5)\text{ } \overline{AN}\cong\overline{AN}` Reflexive Property.

`6)\text{ } \Delta AMN\cong \Delta NOA` SSS Congruence.

Notes: AAA and SAA are not theorems of congruence.