Cailyn knows that if two angles are vertical, they are congruent. she also knows that if two angles are congruent, then they have the same measure. she is given vertical angles 1 and 2, and she concludes that m∠1 = m∠2. what law of reasoning does she use?

 Law of syllogism

Step-by-step explanation:

Since she is given that ∠1 and ∠2 are vertical angles.

⇒∠1=∠2 [ Since she knows that if two angles are vertical, they are congruent. ]

⇒ m∠1 = m∠2[Since she knows that if two angles are congruent, then they have the same measure.]

Therefore by law of syllogism, if ∠1 and ∠2 are vertical angles then m∠1 = m∠2.

The law of syllogism is a valid argument form of deductive reasoning .It is similar to the transitive property of equality, which reads: if a = b and b = c then, a = c.

d

step-by-step explanation:

by observation, we can see that the the graph is simply the graph of y = |x| that has been shifted 4 units downwards and 3 units to the left.

we can recognize in choice d :

y = | x + 3 |   - 4 (rewriting in general form)

y = | x - (- 3) |   - 4

the "-4 " term means   that the graph has been shifted by 4 units in the negative y direction

the "-3 " term means   that the graph has been shifted by 3 units in the negative x direction

this matches our observation of the graph described above.

step-by-step explanation: