1. provide reasons for the statements.

given: ∠1 and ∠3 are vertical angles.

prove: ∠1 ≅ ∠3



statement reason
1. ∠1 and ∠3 are vertical angles. 1. given
2. ∠1 and ∠2 form a linear pair.
∠2 and ∠3 form a linear pair. 2. definition of linear pair
3. ∠1 and ∠2 are supplementary.
∠2 and ∠3 are supplementary. 3.
4. m∠1 + m∠2 = 180˚
m∠2 + m∠3 = 180˚ 4.
5. m∠1 + m∠2 = m∠2 + m∠3 5.
6. m∠1 = m∠3 6.
7. ∠1 ≅ ∠3 7. given

2. in the figure, point b is the midpoint of ac. use the figure to answer the questions.

(a) jeremy says that △abd ≅ △cbd by the sas congruence postulate. do you agree or disagree? explain.

(b) suppose it is also known that ad ≅ cd. which postulate or theorem can be used to prove that △abd ≅ △cbd? justify your answer.


3. use rigid motions to explain whether the triangles in the figure are congruent. be sure to describe specific rigid motions in your explanation.

the picture goes in the same order as the questions. the 1, 2, 3, 4 picture goes with question one, the upside down triangles goes with question 2 and the graph goes with question 3.

need don't know any of these, i need with these questions asap before 11: 59 p. m. you