When writing a geometric proof, which angle relationship could be used alone to justify that two angles are congruent?
2 answers:
Answer:
Vertical angles are always congruent.
Step-by-step explanation:
Vertical angles are always congruent, but congruent angles do not have to be vertical. Any two angles with the same angle measurement are considered congruent by definition.
Imagine (or draw):
an X forming 2 pairs of vertical angles. ∠1 is to the left, ∠2 is on top, ∠3 is to the right, and ∠4 is on the bottom. Vertical angles are always congruent because ∠1 and ∠2 are supplementary, meaning that their measures add to 180 degrees. The measures of ∠2 and ∠3 also add to 180 degrees. This means that:
m∠1+m∠2=180 and m∠2+m∠3=180.
Using the Transitive Property, it becomes m∠1+m∠2=m∠2+m∠3.
If you subtract the measure of ∠2 from both sides,
it becomes m∠1=m∠3
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Answer:
x = 3 + √6 ; x = 3 - √6 ; ;
Step-by-step explanation:
Relation given in the question:
(x² − 6x +3)(2x² − 4x − 7) = 0
Now,
for the above relation to be true the following condition must be followed:
Either (x² − 6x +3) = 0 ............(1)
or
(2x² − 4x − 7) = 0 ..........(2)
now considering the equation (1)
(x² − 6x +3) = 0
the roots can be found out as:
for the equation ax² + bx + c = 0
thus,
the roots are
or
or
and, x =
or
and, x =
or
x = 3 + √6 and x = 3 - √6
similarly for (2x² − 4x − 7) = 0.
we have
the roots are
or
or
and, x =
or
and, x =
or
and, x =
or
and,
Hence, the possible roots are
x = 3 + √6 ; x = 3 - √6 ; ;