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Answer: D) If two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent.
Step-by-step explanation:
Since, By the Alternative interior angle theorem,
When two parallel lines are cut by the same transversal then the alternative interior angles made by the transversal on these parallel lines are congruent to each other.
Here AC ║ A'C'
⇒ AD ║ A'C'
⇒ parallel lines AD and A'C are cut by the same transversal A'D
⇒ ∠ CDB' ≅ ∠ BA'C' -------(1)
Similarly, When, AB ║ A'B
⇒ AB ║ A'D and AB ║EB'
⇒ Parallel lines AB and A'D are cut by the same transversal AD and Parallel lines AB and EB' are cu by the same transversal EB.
⇒ ∠ BAC ≅ ∠CDB' ------(2) and ∠ABC ≅ ∠BEB' -------(3)
Also, BC ║ B'C'
⇒ BE ║ B'C'
And, these paralle lines are cut by the same transversal B'E,
Thus, ∠BEB' ≅ ∠ A'B'C' ---------(4)
Thus, By equations (1) and (2),
∠ BAC ≅ ∠B'A'C ( By transitive property of equality )
And, By equation (3) and (4),
∠ABC ≅ ∠ A'B'C' ( By transitive property of equality )
Answer:
The least common multiple (LCM) of two or more non-zero whole numbers is the smallest whole number that is divisible by each of those numbers. In other words, the LCM is the smallest number that all of the numbers divide into evenly.
Step-by-step explanation:
The LCM of 13 AND 17 is 221
The LCM of 40 AND 60 is 120
lcm (40; 60) = 120 = 23 × 3 × 5
