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Question
written exercises
in exercises 1 - 6 you are given a diagram that is marked with given information.
give the reason for each key step of the proof.
a 1. prove: \\( \overline { n e } \cong \overline { o s } \\)
key steps of proof:
a. \\( \triangle r n x \cong \triangle l o y \\)
b. \\( \angle x \cong \angle y \\)
c. \\( \triangle n e x \cong \triangle o s y \\)
d. \\( \overline { n e } \cong \overline { o s } \\)
- prove: \\( \overline { b e } \cong \overline { d f } \\)
key steps of proof:
a. \\( \triangle a b c \cong \triangle c d a \\)
b. \\( \angle 1 \cong \angle 2 \\)
c. \\( \triangle a b e \cong \triangle c d f \\)
d. \\( \overline { b e } \cong \overline { d f } \\)
1.
- a. If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent (SSS).
- b. Corresponding parts of congruent triangles are congruent (CPCTC).
- c. If two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, then the triangles are congruent (AAS).
- d. Corresponding parts of congruent triangles are congruent (CPCTC).
2.
- a. If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent (SSS).
- b. Corresponding parts of congruent triangles are congruent (CPCTC).
- c. If two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, then the triangles are congruent (AAS).
- d. Corresponding parts of congruent triangles are congruent (CPCTC).
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1.
- a. SSS (Side - Side - Side) congruence criterion.
- b. CPCTC (Corresponding Parts of Congruent Triangles are Congruent).
- c. AAS (Angle - Angle - Side) congruence criterion.
- d. CPCTC (Corresponding Parts of Congruent Triangles are Congruent).
2.
- a. SSS (Side - Side - Side) congruence criterion.
- b. CPCTC (Corresponding Parts of Congruent Triangles are Congruent).
- c. AAS (Angle - Angle - Side) congruence criterion.
- d. CPCTC (Corresponding Parts of Congruent Triangles are Congruent).