Question

lesson 5.2/5.3 congruent polygons, triangle congruence sas

1. each part of a figure is mapped to a corresponding part of its image by a
2. third angles theorem: if two angles of one triangle are congruent to two angles of another triangle,

then the third angles are also

1. if two sides and the included angle of one triangle are congruent to those of another triangle, then the

triangles are congruent by

1. name the property: for any triangle \\( \triangle a b c, \triangle a b c \cong \triangle a b c \\)
2. name the property: if \\( \triangle a b c \cong \triangle d e f \\), then \\( \triangle d e f \cong \triangle a b c \\)
3. name the property: if \\( \triangle a b c \cong \triangle d e f \\) and \\( \triangle d e f \cong \triangle j k l \\), then \\( \triangle a b c \cong \triangle j k l \\)
4. two angles that lie outside the two lines and on opposite sides of the transversal are
5. two angles that lie between the two lines and on opposite sides of the transversal are
6. two angles with corresponding positions are
7. two angles that lie between the two lines and on the same side of the transversal are called

Explanation:

1. In geometry, when a figure is transformed (like translation, rotation, reflection), each part is mapped by a transformation.
2. The Third Angles Theorem in triangle congruence states if two angles are congruent, the third are congruent.
3. The SAS (Side - Angle - Side) congruence criterion for triangles.
4. The reflexive property of congruence (a figure is congruent to itself).
5. The symmetric property of congruence (if \(A\cong B\), then \(B\cong A\)).
6. The transitive property of congruence (if \(A\cong B\) and \(B\cong C\), then \(A\cong C\)).
7. Definition of alternate exterior angles.
8. Definition of alternate interior angles.
9. Definition of corresponding angles.
10. Definition of consecutive interior angles.

Answer:

1. transformation
2. congruent
3. SAS (Side - Angle - Side)
4. Reflexive Property of Congruence
5. Symmetric Property of Congruence
6. Transitive Property of Congruence
7. alternate exterior angles
8. alternate interior angles
9. corresponding angles
10. consecutive interior angles