Question

triangles with corresponding angles that are equal and corresponding sides that are proportional are called
triangles that are identical in both shape and size are called
the point where the perpendicular bisectors of a triangles sides intersect is called the
the point where the angle bisectors of a triangle intersect is called the
the point where the altitudes of a triangle intersect is called the
the point where the medians of a triangle intersect is called the
the theorem stating that the sum of the lengths of any two sides of a triangle is greater than the length of the third side is called the
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
the perpendicular bisector theorem states that any point on the perpendicular bisector of a segment is from the segments endpoints.
the angle bisector theorem states that the angle bisector divides the opposite side into segments to the other two sides.

Explanation:

1. Similar triangles have equal corresponding angles and proportional corresponding sides.
2. Congruent triangles are identical in shape and size.
3. The circumcenter is the intersection of perpendicular bisectors.
4. The incenter is the intersection of angle bisectors.
5. The orthocenter is the intersection of altitudes.
6. The centroid is the intersection of medians.
7. The triangle inequality theorem states the sum of two sides is greater than the third.
8. AA (Angle - Angle) criterion is for triangle similarity with two equal angles.
9. A median connects a vertex to the mid - point of the opposite side.
10. An altitude is a perpendicular from a vertex to the opposite side's line.
11. The centroid divides each median in a 2:1 ratio.
12. AAS (Angle - Angle - Side) is another congruence criterion.
13. SAS (Side - Angle - Side) is a congruence criterion.
14. The Perpendicular Bisector Theorem states equal distance from endpoints.
15. The Angle Bisector Theorem states proportional segments.

Answer:

1. Similar triangles
2. Congruent triangles
3. Circumcenter
4. Incenter
5. Orthocenter
6. Centroid
7. Triangle inequality theorem
8. AA (Angle - Angle) criterion
9. Median
10. Altitude
11. Centroid
12. AAS (Angle - Angle - Side)
13. SAS (Side - Angle - Side)
14. Equidistant
15. Proportional