Question

can one of the triangle congruence theorem listed below be used to show the two triangles are congruent? (1 point) a angle - side - angle theorem b side - angle - side theorem c side - side - side theorem d none of the theorems listed can be used to show congruence

Explanation:

• The Angle - Side - Angle (ASA) congruence theorem requires two angles and the included side of one triangle to be equal to two angles and the included side of another triangle.
• The Side - Angle - Side (SAS) congruence theorem requires two sides and the included angle of one triangle to be equal to two sides and the included angle of another triangle.
• The Side - Side - Side (SSS) congruence theorem requires all three sides of one triangle to be equal to all three sides of another triangle.
• In the given figure, we have two angles (∠A and ∠D) and a non - included side (the sides marked equal are not between the two given angles).
• The Angle - Side - Angle (ASA) theorem is not applicable as the side is not included between the two angles.
• The Side - Angle - Side (SAS) theorem is not applicable as the angle is not included between the two sides.
• The Side - Side - Side (SSS) theorem is not applicable as we only know about one pair of sides (from the marks) and two angles.

Answer:

D. None of the theorems listed can be used to show congruence