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masha68 [24]
3 years ago
10

Which of the following theorems cannot be used to prove two lines are parallel?

Mathematics
1 answer:
mariarad [96]3 years ago
6 0

Answer:

Option H

Step-by-step explanation:

Option F

If two lines are cut by a transversal so that a pair of corresponding angles are congruent, then the lines are parallel.

True.

Option G

If two lines are cut by a transversal so that a pair of alternate exterior angles are congruent, then the lines are parallel.

True

Option H

If two line are cut by a transversal so that a pair of vertical angles are congruent, then the lines are parallel.

Since, vertical angles don't prove the lines cut by a transversal are parallel.

So the statement is False.

Option J

If two lines are are cut by a transversal so that a pair of same side interior angles are supplementary, then the lines are parallel.

True.

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Answer:

EBGA

Step-by-step explanation:

The triangle is isosceles (XZ = YZ), so the base angles are congruent.  The total of all three angles in the triangle is 180 degrees, so subtracting out 52 leaves 128 degrees for the two base angles together.  Each base angles measures half of that, so m\angle 1 = 64^\circ, code E.

Look at vertex Y.  The big angle there also measures 64 degrees.

m\angle 2 + 31^\circ =64^\circ\\m\angle 2= 64^\circ - 31^\circ = 33^\circ \text{ (code B)}

Angle 3 is a vertical angle with the 88 degree angle, so its measure is also 88 degrees (code G).

Finally, angle 4 is an exterior angle in the small triangle that contains angles 2 and 3.  In that triangle, angles 2 and 3 are the remote interior angles.

m\angle 4 = m\angle 2 + m\angle 3\\m\angle 4 = 33^\circ + 88^\circ = 121^\circ \text{  (code A)}

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