Question

asa/aas
determine if the two triangles are congruent. if they are, state how you know.
1)
2)
3)
4)
5)
6)

Explanation:

1)

• Step1: Check congruence criteria
• For triangle congruence, we have ASA (Angle - Side - Angle) and AAS (Angle - Angle - Side) criteria. In the first figure, we do not have enough information (two angles and a non - included side or two angles and the included side) to prove congruence.

2)

• Step1: Identify angles and side
• We have two angles (the given angles) and a non - included side (the side of length 5). By the AAS (Angle - Angle - Side) congruence criterion.

3)

• Step1: Analyze the given elements
• We have two angles (the given angles) and a non - included side (the side of length 5). By the AAS (Angle - Angle - Side) congruence criterion.

4)

• Step1: Examine the triangle parts
• We have two angles (the vertical angles are equal) and a non - included side (the given sides of lengths 4 and 5). But we do not have two pairs of corresponding angles and a non - included side in the correct order for AAS or ASA.

5)

• Step1: Look at the right - angled triangles
• We have a right angle (90 degrees), a side (marked with the same length) and another angle (the vertical angles are equal). By the AAS (Angle - Angle - Side) congruence criterion.

6)

• Step1: Check the ASA criterion
• We have two angles (the given angles) and the included side (the side between the two angles). By the ASA (Angle - Side - Angle) congruence criterion.

Answer:

1. Not congruent.
2. Congruent by AAS.
3. Congruent by AAS.
4. Not congruent.
5. Congruent by AAS.
6. Congruent by ASA.