Introduction to Congruence

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Show your work for each problem.

1.
What does it mean when two shapes are congruent?
1. a)They have the same number of sides
2. b)They have the same size and shape
3. c)They have the same color
4. d)They have the same angles only
2.
Which symbol is used to show that two figures are congruent?
1. a)
2. b)
3. c)
4. d)
3.
Triangle ABC has sides 4 cm, 6 cm, and 8 cm. Triangle DEF is congruent to ABC. What is the length of the longest side of triangle DEF (in cm)?
4.
Two triangles have the same three angles. Are they definitely congruent?
1. a)Only if one angle is 90 degrees
2. b)Yes, same angles means congruent
3. c)No, they could be different sizes
4. d)Only if they have 3 sides
5.
Rectangle ABCD is congruent to rectangle EFGH. If rectangle ABCD has a perimeter of 24 cm, what is the perimeter of rectangle EFGH (in cm)?
6.
A shape is rotated 90 degrees. Is the rotated shape congruent to the original?
1. a)No, the orientation changed
2. b)Only for squares
3. c)Only if it is rotated 180 degrees
4. d)Yes, rotation preserves congruence
7.
Triangle ABC has angles , , and . Triangle DEF has the same angles. Are they congruent? Explain.
8.
. If angle A = and angle B = , what is the measure of angle F (in degrees)?
9.
Which transformation does NOT preserve congruence?
1. a)Reflection
2. b)Translation
3. c)Dilation (scaling)
4. d)Rotation
10.
Quadrilateral ABCD has sides 3 cm, 5 cm, 3 cm, 5 cm. Quadrilateral EFGH has sides 3 cm, 5 cm, 3 cm, 5 cm. Are they congruent?
11.
. If side AB = 12 cm, what is the length of side XY (in cm)?
12.
Triangle ABC has sides 5 cm, 12 cm, and 13 cm. Triangle DEF has sides 5 cm, 12 cm, and 13 cm. Are the triangles congruent? Explain why.
13.
A shape is reflected, then rotated 180 degrees. Is the final shape congruent to the original?
1. a)Only if the shape is symmetric
2. b)No, two transformations cancel out
3. c)Yes, both are rigid transformations
4. d)No, reflections change congruence
14.
. The area of is 24 square cm. What is the area of (in square cm)?
15.
Square ABCD has side length 5 cm. Rectangle EFGH has length 5 cm and width 5 cm. Are they congruent?
16.
Two circles have the same radius of 4 cm. Are they congruent?
1. a)Only if they are in the same position
2. b)Only if they have the same center
3. c)Yes, same radius means same size and shape
4. d)No, circles cannot be congruent
17.
Equilateral triangle ABC is congruent to equilateral triangle DEF. If the perimeter of ABC is 27 cm, what is the side length of DEF (in cm)?