Congruent Triangles

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Show your work for each problem.

1.
Two triangles are congruent. What can you conclude?
1. a)They have the same shape but different sizes
2. b)They have the same shape and size
3. c)They have neither the same shape nor size
4. d)They have different shapes but the same size
2.
Which criterion uses three pairs of equal sides to prove congruence?
1. a)SAS
2. b)ASA
3. c)AAS
4. d)SSS
3.
For SAS congruence, where must the angle be located?
1. a)Opposite to the longer side
2. b)Outside the triangle
3. c)Between the two sides
4. d)At any vertex
4.
If and cm, what is the length of in cm?
5.
In congruent triangles, . If corresponds to , what is in degrees?
6.
Which is NOT a valid criterion for proving triangle congruence?
1. a)SSS (Side-Side-Side)
2. b)AAA (Angle-Angle-Angle)
3. c)SAS (Side-Angle-Side)
4. d)ASA (Angle-Side-Angle)
7.
Triangles have: cm, cm, and . Can you prove they are congruent?
1. a)Yes, by ASA
2. b)Yes, by SAS
3. c)Yes, by SSS
4. d)No, this is SSA which doesn't prove congruence
8.
Two triangles are congruent by SSS. The sides of the first triangle are 6 cm, 8 cm, and 10 cm. What is the perimeter of the second triangle in cm?
9.
Given: cm, , . Which criterion proves ?
10.
Right triangles ABC and DEF have right angles at B and E. If cm and cm, prove they are congruent.
11.
In , and . If , what is in degrees?
12.
Why is HL (Hypotenuse-Leg) a valid criterion but SSA (Side-Side-Angle) is not?
1. a)HL requires a 90-degree angle which eliminates the ambiguous case
2. b)SSA can only be used for acute triangles
3. c)HL uses more information than SSA
4. d)HL was invented after SSA was disproven
13.
In quadrilateral ABCD, diagonal AC divides it into triangles ABC and ACD. If , , and is shared, prove .
14.
Two congruent triangles have areas of 24 cm each. If one triangle has a base of 8 cm, what is the height of the other triangle to a corresponding base in cm?
15.
Given: , , cm. Prove and find the criterion.