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Triss [41]
3 years ago
15

In the straightedge and compass construction of the parallel line below, which of the following reasons can you use to prove tha

t CD and EG are parallel?
A. ∠FCD ≅ ∠FDC by construction
B. ∠FEG≅ ∠FGE by construction
C. ∠FCD ≅ ∠GEC by construction
D. ∠FEG ≅ ∠FCD by construction

Mathematics
1 answer:
Eva8 [605]3 years ago
3 0

Answer:

D.

Step-by-step explanation:

Lines EG and CD are cut by transversal CF.

By construction, ∠FEG=∠FCD. These two angles are corresponding angles.

Since two corresponding angles are congruent, then lines EG and CD are parallel (by  converse of the corresponding angles postulate).

Converse of the Corresponding Angles Postulate: If the corresponding angles formed by two lines and a transversal are congruent, then lines are parallel.

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9514 1404 393

Answer:

  ∠CAB = 28°

  ∠DAC = 64°

Step-by-step explanation:

What you do in each case is make use of the relationships you know about angles in a triangle and around parallel lines. You can also use the relationships you know about diagonals in a rectangle, and the triangles they create.

<u>Left</u>

Take advantage of the fact that ∆AEB is isosceles, so the angles at A and B in that triangle are the same. If we call that angle measure x, then we have the sum of angles in that triangle is ...

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The measure of angle CAB is 28°.

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<u>Right</u>

Sides AD and BC are parallel, so diagonal AC can be considered a transversal. The two angles we're concerned with are alternate interior angles, so are congruent.

  ∠BCA = ∠DAC = 64°

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8 0
3 years ago
How do i solve this because I need some help. I'm studying for my test.
mote1985 [20]
At Gino's you pay $16 plus $8 per pizza.
At Venetian's you pay $24 plus $6 per pizza.
Let the number of pizzas be x.

At Gino's you pay 16 + 8x
At Venetian's you pay 24 + 6x

Set the two costs equal and solve for x to find out the number of pizzas for which both costs are the same.

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x = 4
Each place gives you a free pizza.
4 pizzas plus the free pizza equals 5 pizzas.

If you need 5 pizzas (including the free one), both parlors cost the same.

If you need fewer than 5 pizzas, use Gino's.
If you need more than 5 pizzas, use Venetian's.
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