Proving the Converse of the Side-Splitter Theorem C 0
Given: AD= BE
Prove: AB DE
Statements
Reasons
1. given
1.00 - E
2.62 +1 = € +1
3. O + DE = € + EC
2. addition property
A
D
3. property of proportion
С
2
E
1
BEEC
EC
4. addition of fractions
B
4
AD | DC
DC
5. AC = AD + DC
BC = BE + EC
5. segment addition
postulate
Complete the steps of the proof.
6. AC = BC
6. substitution property
7.232 23
7. reflexive property
8. AABC - ADEC
8.4
9. 21 22
9.
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1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?