Question

question: 4
prove this theorem: if a quadrilateral is a parallelogram, then the opposite sides are. find the coordinates for point r that proves figure trap is an isosceles trapezoid.
she draws parallelogram abcd with diagonal ac to start her proof.

statement reason

1. abcd is a parallelogram. given
2. ab || cd and bc || ad definition of parallelogram
3. ∠1 ≅ ∠4 alternate interior angles theorem
4. ∠2 ≅ ∠3 alternate interior angles theorem
5. ac ≅ ac reflexive property of congruence
6. △abc ≅ △cda
7. bc ≅ da and ab ≅ cd corresponding parts of congruent triangles are congruent.

which of the following is the missing reason for statement six in the proof?
a. asa
b. sss
find the coordinates for point r that proves figure trap is an isosceles trapezoid. t (a, b), p, a (c, 0)
a. (a, c - b)
b. (2a, b)
c. (c - a, b)
d. (c - 2a, b)

Explanation:

We have two - angles and the included side congruent. From statements 3 ($\angle1\cong\angle4$), 4 ($\angle2\cong\angle3$) and 5 ($\overline{AC}\cong\overline{AC}$), we use the Angle - Side - Angle (ASA) congruence criterion to prove $\triangle ABC\cong\triangle CDA$.

Answer:

A. ASA