justify the last two steps of the proof.
Given: ABCD is a parallelogram.
Prove: triangleABC = triangleCDA
1. ABDC is a parallelogram 1. given
2. AB = DC and BC =DC 2. opposite sides of a parallelogram are congruent
3. AC = CA 3. ?
4. triangleABC = triangleCDA 4.?
last two are 3 and 4. g
D. Reflexive Property of SSS
like seriously tho, there's got to be teachers in disguise as a student to not let students know the answer. yikesss
@MathMate that doesn't help. im not signing up
@SherryKnows i wouldnt be suprized
To justify the last two steps of the proof, we need to use the properties of triangles and the information given in the problem.
Step 3: AC = CA
To justify this step, we can use the property of congruent sides in a triangle. In triangle ABC, we have AB = DC and BC = DC (as given in step 2). Now, if we connect points A and C, we can consider triangle ACB. Since AB = DC and BC = DC, we can say that AC = CA by the property of congruent sides. Therefore, AC = CA is justified.
Step 4: triangleABC = triangleCDA
To justify this step, we can use the property of triangle congruence. In step 1, it is given that ABCD is a parallelogram. Since opposite sides of a parallelogram are congruent, we have AB = DC and BC = DA. In step 2, we showed that AC = CA. Now, if we consider triangle ABC and triangle CDA, we have AB = DC, BC = AD, and AC = CA. These are three pairs of corresponding sides that are congruent. Therefore, by the side-side-side (SSS) congruence criterion, we can conclude that triangle ABC is congruent to triangle CDA, which justifies the step triangleABC = triangleCDA.
In conclusion, step 3 is justified using the property of congruent sides in a triangle, and step 4 is justified using the SSS congruence criterion for triangles.
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hint:
http://study.com/academy/lesson/reflexive-property-of-congruence-definition-examples.html