How are the SAS Postulate and SSS Postulate alike? Check all that apply.
A.They both require three congruency statements.
B.They both use two sides and one angle.
C.They both use one side and two angles.
D.They both can be used to prove that triangles are congruent.
E.They both use three sides.
How are the SAS Postulate and SSS Postulate different? Check all that apply.
A.They require different numbers of congruency statements.
B.They apply to different kinds of triangles (acute or obtuse).
C.They use different numbers of sides and/or angles.
D.SSS can be used to prove two triangles are congruent, while SAS can be used to prove that corresponding angles are congruent.
To determine how the SAS Postulate and SSS Postulate are alike, we can analyze the options provided:
A. They both require three congruency statements.
This statement is correct. Both the SAS (Side-Angle-Side) Postulate and the SSS (Side-Side-Side) Postulate require stating three congruency statements between corresponding sides or angles of two triangles.
D. They both can be used to prove that triangles are congruent.
This statement is also correct. Both the SAS Postulate and the SSS Postulate can be used to prove the congruence of two triangles.
E. They both use three sides.
This statement is incorrect. Unlike the SSS Postulate, which indeed uses three sides, the SAS Postulate uses two sides and the included angle between them.
Therefore, the correct options for the similarities between the SAS Postulate and the SSS Postulate are A and D.
Now, let's determine the differences between the two postulates:
A. They require different numbers of congruency statements.
This statement is correct. The SAS Postulate requires stating two sides and the included angle, whereas the SSS Postulate requires stating three corresponding sides.
B. They apply to different kinds of triangles (acute or obtuse).
This statement is not applicable. Both the SAS Postulate and the SSS Postulate can be applied to all types of triangles, whether they are acute or obtuse.
C. They use different numbers of sides and/or angles.
This statement is correct. The SAS Postulate uses two sides and one angle, while the SSS Postulate uses three sides.
D. SSS can be used to prove two triangles are congruent, while SAS can be used to prove that corresponding angles are congruent.
This statement is correct. The SSS Postulate can be used to directly prove the congruence of two triangles, while the SAS Postulate can be used to prove that corresponding angles of congruent triangles are congruent.
Therefore, the correct options for the differences between the SAS Postulate and the SSS Postulate are A, C, and D.