Question

the criterion used to prove the similarity of triangles by showing that two pairs of corresponding angles are equal is known as

a line segment from a vertex of a triangle to the midpoint of the opposite side is called a

a perpendicular segment from a vertex of a triangle to the line containing the opposite side is called an

the intersection point of the medians of a triangle, which divides each median into a 2:1 ratio, is called the

triangles are proven congruent using criteria such as sas, sss, asa, and

the criterion used to prove the congruence of triangles when two sides and the included angle are equal is known as

Explanation:

1. The AA (Angle - Angle) similarity criterion states that if two pairs of corresponding angles in two triangles are equal, the triangles are similar.
2. A line segment from a vertex of a triangle to the mid - point of the opposite side is a median.
3. A perpendicular segment from a vertex of a triangle to the line containing the opposite side is an altitude.
4. The centroid of a triangle is the intersection point of its medians and divides each median in a 2:1 ratio.
5. The AAS (Angle - Angle - Side) is another criterion for proving triangle congruence along with SAS, SSS, ASA.
6. The SAS (Side - Angle - Side) criterion is used to prove triangle congruence when two sides and the included angle are equal.

Answer:

1. AA (Angle - Angle) similarity criterion
2. Median
3. Altitude
4. Centroid
5. AAS (Angle - Angle - Side)
6. SAS (Side - Angle - Side)