ASA and AAS Congruence

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Show your work for each problem.

1.
In the ASA congruence theorem, what does the 'S' stand for?
1. a)Sum
2. b)Side (between the angles)
3. c)Straight
4. d)Similar
2.
What is the key difference between ASA and AAS?
1. a)Position of the known side relative to the angles
2. b)Size of the angles
3. c)Type of triangle
4. d)Number of angles known
3.
Why can't AAA (three angles) prove triangle congruence?
1. a)Angles don't determine shape
2. b)Three angles are not enough information
3. c)It only works for right triangles
4. d)Triangles can have equal angles but different sizes
4.
In triangle , and . What is ?
5.
Triangle has and . What is ?
6.
Triangle has , , cm. Triangle has , , cm. Which theorem proves congruence?
1. a)ASA
2. b)SAS
3. c)AAS
4. d)SSS
7.
Triangle has , , cm. Triangle has , , cm. Which theorem proves congruence?
1. a)ASA
2. b)SSS
3. c)AAS
4. d)SAS
8.
If by ASA with , , what is in degrees?
9.
Determine if the triangles are congruent: with , , cm and with , , cm.
10.
Determine the theorem: with , , cm and with , , cm.
11.
Triangle has , . Triangle has , . If , can you prove the triangles congruent?
1. a)Yes, by SAS
2. b)No, the angles don't match
3. c)Yes, by ASA
4. d)Yes, by AAS
12.
Two triangles are congruent by AAS. Triangle 1 has angles and with the side opposite the angle measuring cm. What is the length of the corresponding side in Triangle 2?
13.
Given: and where , , and . Prove the triangles are congruent and identify the theorem used.
14.
In , , , cm. In , , , cm. Find all side lengths of if cm and cm.
15.
Why is AAS actually just a special case of ASA?
1. a)Both only need two measurements
2. b)They use the same number of pieces of information
3. c)Knowing two angles determines the third, so you actually know the included angle
4. d)They are completely different theorems