1. 2-5Postulates and Paragraph Proofs Day 2
Write paragraph proofs

2. Paragraph Proof
A paragraph proof is one method of proving statements and conjectures. It involves writing a paragraph to explain why a conjecture for a given situation is true. Paragraph proofs are also called informal proofs. This does not mean that this form of proof is any less valid than the other types of proofs.

3. Page 129 in your book.

4. Write a paragraph proof
Given:
Prove: ACD is a plane.
Proof: and must intersect at C because if two lines intersect, then their intersection is exactly one point. Point A is on and point D is on Points A, C, and D are not collinear. Therefore, ACD is a plane as it contains three points not on the same line.

6. Proof: ?

7. Choose the best reason to complete the proof.
A. Definition of midpoint
B. Segment Addition Postulate
C. Definition of congruent segments
D. Substitution

8. Given that M is the midpoint of 𝑋𝑌 , write a paragraph proof to show that
𝑋𝑀 ≅ 𝑀𝑌
Given: M is the midpoint of 𝑋𝑌.
Prove 𝑋𝑀 ≅𝑀𝑌
STEP 1 X M Y
STEP 2
If M is the midpoint of 𝑋𝑌 , then from the definitions of midpoint of a segment, we know that XM + MY. This means that 𝑋𝑀 and 𝑀𝑌 have the same measure. By the definition of congruence, if two segments have the same measure, then they are congruent.
Thus, 𝑋𝑀 ≅ 𝑀𝑌 .
STEPS 3 & 4
STEP 5

9. Once a conjecture is proven true, it can be states as a theorem and used in other proofs.
Therefore, a theorem is a conjecture that has been proven true.
Page 129 in your book

10. 2-5 Assignment Day 2
Page 131, 34-42