Question

1. define complementary and supplementary angles?
2. angles in a triangle add up to:
3. identify the type of angles shown:

a) angles f and i:
b) angles h and k:
c) angles f and j:
d) angles l and m:

1. if two shapes are congruent, what does that mean?
2. write two true statements about the angles shown below:
3. describe a unique shape?
4. write two true statements about rigid transformations and congruence
5. if angle bad is 80°, what is the measure of

true or false:

1. angles bad and aeg are congruent?
2. angles aef and bad are congruent?

Explanation:

1. Complementary angles are two angles whose sum is 90°. Supplementary angles are two angles whose sum is 180°.
2. The sum of interior - angles of a triangle is a fundamental geometric fact, always 180°.
3. a) Vertical angles are equal and opposite. b) Corresponding angles are in the same relative position. c) Alternate exterior angles are on the outside and opposite sides. d) Adjacent angles share a common side.
4. Congruent shapes have the same size and shape.
5. a) Angle a and the 45° angle are vertical angles, so a = 45°. b) Angle a and angle c are supplementary, so c=135°.
6. A unique shape could be a regular pentagon, which has 5 equal sides and 5 equal angles.
7. Rigid transformations (translation, rotation, reflection) preserve shape and size. Congruent shapes can be mapped onto each other by rigid transformations.
8. (No full information for this part).
9. (No full information about the position of angles BAD and AEG to determine).
10. (No full information about the position of angles AEF and BAD to determine).

Answer:

1. Complementary angles: Two angles with a sum of 90°. Supplementary angles: Two angles with a sum of 180°.
2. 180°
3. a) Vertical angles

b) Corresponding angles
c) Alternate exterior angles
d) Adjacent angles

1. They have the same size and shape.
2. a) Angle a = 45°

b) Angle c = 135°

1. A regular pentagon has 5 equal - length sides and 5 equal interior angles.
2. Rigid transformations preserve shape and size. Congruent shapes can be related by rigid transformations.
3. (Incomplete information)
4. (Incomplete information)
5. (Incomplete information)