Consumer Reports is conducting tests to determine the distance a certain car model will travel on one gallon of gas. In a sample
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Answer:
Step-by-step explanation:
Consider triangle ACD. This triangle is isosceles triangle, because AD = DC. Angles adjacent to the base AC are congruent abgles, so
The sum of the measures of all interiror angles in the triangle is always then
Angles ADC and BDC are supplementary angles (add up to ), then
Consider triangle BCD. This triangle is isosceles triangle because BC = DC. Angles adjacent to the base BD are congruent abgles, so
The sum of the measures of all interiror angles in the triangle is always then
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 )
