Question

name the postulate, if possible, that makes the triangles congruent. not possible asa sas sss

Explanation:

To determine the congruence postulate, we analyze the marked sides and angles:

1. Identify Marked Parts:

• Triangle \( ABC \) (left) and triangle \( DEF \) (right) have:
• One pair of sides with one tick mark (congruent).
• One pair of sides with three tick marks (congruent).
• Both triangles are right triangles (right angles at \( A \) and \( E \), marked by the right-angle symbol), so the right angles are congruent.

1. Analyze Congruence Postulates:

• SAS (Side - Angle - Side): Requires two sides and the included angle to be congruent. Here, the right angle is the included angle between the two marked sides (one pair with one tick, one pair with three ticks) in each triangle.
• ASA (Angle - Side - Angle): Requires two angles and the included side, which does not match here.
• SSS (Side - Side - Side): Requires three sides, but we only have two sides marked (plus a right angle, not a third side).

Since we have two sides and the included right angle congruent, the SAS postulate applies.

Final Answer: SAS

Answer:

To determine the congruence postulate, we analyze the marked sides and angles:

1. Identify Marked Parts:

• Triangle \( ABC \) (left) and triangle \( DEF \) (right) have:
• One pair of sides with one tick mark (congruent).
• One pair of sides with three tick marks (congruent).
• Both triangles are right triangles (right angles at \( A \) and \( E \), marked by the right-angle symbol), so the right angles are congruent.

1. Analyze Congruence Postulates:

• SAS (Side - Angle - Side): Requires two sides and the included angle to be congruent. Here, the right angle is the included angle between the two marked sides (one pair with one tick, one pair with three ticks) in each triangle.
• ASA (Angle - Side - Angle): Requires two angles and the included side, which does not match here.
• SSS (Side - Side - Side): Requires three sides, but we only have two sides marked (plus a right angle, not a third side).

Since we have two sides and the included right angle congruent, the SAS postulate applies.

Final Answer: SAS