Question

two triangles are similar by the ______ rule if they have two angles of the same measure.
in coordinate geometry, the horizontal axis is typically labeled as the ______ axis.
similar triangles have proportional corresponding ______ as well as congruent corresponding angles.
the principle that allows the use of ratios in similar triangles to find unknown lengths is known as the ______ proportionality.
the term ______ describes the scenario when two triangles are similar and all corresponding sides are in equal proportion.
to prove triangles are similar using coordinates, one often needs to calculate the ______ of the sides using the distance formula.
when using aa similarity to prove the similarity of triangles, one must show that two angles are ______

Explanation:

1. AA (Angle - Angle) similarity rule states that if two angles of one triangle are congruent to two angles of another triangle, the triangles are similar.
2. In a coordinate - plane, the horizontal axis is called the x - axis.
3. Similar triangles have proportional corresponding sides and congruent corresponding angles.
4. The side - side - side (SSS) proportionality principle allows using ratios in similar triangles to find unknown lengths.
5. When all corresponding sides of similar triangles are in equal proportion, it is similarity.
6. To prove triangle similarity using coordinates, the lengths of the sides are calculated with the distance formula.
7. For AA similarity, two angles must be congruent.

Answer:

1. AA (Angle - Angle)
2. x
3. sides
4. Side - Side - Side (SSS)
5. similarity
6. lengths
7. congruent