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{ne}congoverline{os} )
key steps of proof:
a. ( \triangle rnxcong\triangle loy )
b. ( angle xcongangle y )
c. ( \triangle nexcong\triangle osy )
d. ( overline{ne}congoverline{os} )

1. prove: ( overline{be}congoverline{df} )

key steps of proof:
a. ( \triangle abccong\triangle cda )
b. ( angle 1congangle 2 )
c. ( \triangle abecong\triangle cdf )
d. ( overline{be}congoverline{df} )

Explanation:

1.

• a. If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent (SSS - Side - Side - Side congruence criterion).
• 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 two triangles are congruent (AAS - Angle - Angle - Side congruence criterion).
• 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 two triangles are congruent (SSS - Side - Side - Side congruence criterion).
• 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 two triangles are congruent (AAS - Angle - Angle - Side congruence criterion).
• d. Corresponding parts of congruent triangles are congruent (CPCTC).

Answer:

1.

• a. If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent (SSS - Side - Side - Side congruence criterion).
• 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 two triangles are congruent (AAS - Angle - Angle - Side congruence criterion).
• 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 two triangles are congruent (SSS - Side - Side - Side congruence criterion).
• 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 two triangles are congruent (AAS - Angle - Angle - Side congruence criterion).
• d. Corresponding parts of congruent triangles are congruent (CPCTC).