Question

1. sas state what additional information is required in order to know that the triangles are congruent for the reason given. 16) aas 17) sss 18) asa 19) asa 20) sss

Explanation:

Step1: Recall triangle - congruence criteria

SAS (Side - Angle - Side) requires two sides and the included angle to be congruent. AAS (Angle - Angle - Side) requires two angles and a non - included side to be congruent. ASA (Angle - Side - Angle) requires two angles and the included side to be congruent. SSS (Side - Side - Side) requires all three sides to be congruent.

Step2: Analyze problem 15

For SAS, we need two sides and the included angle. If we have two sides marked as congruent in the triangles, we need the measure of the included angle between those two sides to be equal in both triangles.

Step3: Analyze problem 16

For AAS, if we have two angles marked as congruent, we need the non - included side to be congruent. We need to identify the non - included side for the given pairs of angles in the two triangles.

Step4: Analyze problem 17

For SSS, we need to know the lengths of all three sides of both triangles. If two sides are already marked as congruent, we need the third side of each triangle to be congruent.

Step5: Analyze problem 18

For ASA, if we have one angle marked as congruent, we need the two sides that form that angle (the included sides) and the other angle adjacent to one of those sides to be congruent.

Step6: Analyze problem 19

For ASA, if we have one angle marked as congruent, we need the two sides that form that angle (the included sides) and the other angle adjacent to one of those sides to be congruent.

Step7: Analyze problem 20

For SSS, if two sides are marked as congruent, we need the third side of each triangle to be congruent.

1. Answer: The measure of the included angle between the two given congruent sides.
2. Answer: The length of the non - included side for the two given congruent angles.
3. Answer: The length of the third side of each triangle.
4. Answer: The other angle and the two included sides for the given congruent angle.
5. Answer: The other angle and the two included sides for the given congruent angle.
6. Answer: The length of the third side of each triangle.

Answer:

Step1: Recall triangle - congruence criteria

SAS (Side - Angle - Side) requires two sides and the included angle to be congruent. AAS (Angle - Angle - Side) requires two angles and a non - included side to be congruent. ASA (Angle - Side - Angle) requires two angles and the included side to be congruent. SSS (Side - Side - Side) requires all three sides to be congruent.

Step2: Analyze problem 15

For SAS, we need two sides and the included angle. If we have two sides marked as congruent in the triangles, we need the measure of the included angle between those two sides to be equal in both triangles.

Step3: Analyze problem 16

For AAS, if we have two angles marked as congruent, we need the non - included side to be congruent. We need to identify the non - included side for the given pairs of angles in the two triangles.

Step4: Analyze problem 17

For SSS, we need to know the lengths of all three sides of both triangles. If two sides are already marked as congruent, we need the third side of each triangle to be congruent.

Step5: Analyze problem 18

For ASA, if we have one angle marked as congruent, we need the two sides that form that angle (the included sides) and the other angle adjacent to one of those sides to be congruent.

Step6: Analyze problem 19

For ASA, if we have one angle marked as congruent, we need the two sides that form that angle (the included sides) and the other angle adjacent to one of those sides to be congruent.

Step7: Analyze problem 20

For SSS, if two sides are marked as congruent, we need the third side of each triangle to be congruent.

1. Answer: The measure of the included angle between the two given congruent sides.
2. Answer: The length of the non - included side for the two given congruent angles.
3. Answer: The length of the third side of each triangle.
4. Answer: The other angle and the two included sides for the given congruent angle.
5. Answer: The other angle and the two included sides for the given congruent angle.
6. Answer: The length of the third side of each triangle.