Answer: 6. d
7. b
8. d
9. c
Step-by-step explanation:
A because two negatives make a positive
Answer:
1. Opposite
2. angle-side-angle criterion
Step-by-step explanation:
Since ABCD is a parallelogram, the two pairs of <u>(opposite)</u> sides (AB¯ and CD¯, as well as AD¯ and BC¯) are congruent. Then, since ∠9 and ∠11 are vertical angles, it can be concluded that ∠9≅∠11. Since ABCD is a parallelogram, AB¯∥CD¯. Since ∠2 and ∠5 are alternate interior angles along these parallel lines, the Alternate Interior Angles Theorem allows that ∠2≅∠5. Since two angles of △AEB are congruent to two angles of △CED, the Third Angles Theorem supports that ∠8≅∠3. Therefore, using the <u>(angle-side-angle criterion)</u>, it can be stated that △AEB≅△CED. Then, applying the definition of congruent triangles, it can be stated that AE¯≅CE¯, which makes E the midpoint of AC¯. Use a similar argument to prove that △AED≅△CEB; then it can be concluded that E is also the midpoint of BD¯. Since the midpoint of both line segments is the same point, the segments bisect each other by definition. Match each number (1 and 2) with the word or phrase that correctly fills in the corresponding blank in the proof.
A parallelogram posses the following features:
1. The opposite sides are parallel.
2. The opposite sides are congruent.
3. It has supplementary consecutive angles.
4. The diagonals bisect each other.
9514 1404 393
Answer:
x = 23.1
Step-by-step explanation:
The parallel lines make the left segments proportional to the right segments. This lets us write the equation ...
x/14 = 33/20
Multiplying by 14, we get ...
x = 14(33/20) = 7(33/10) = 23.1
Answer:
(3, -3)
Step-by-step explanation:
When asked to solve by elimination, you put them on top of one another, like you're going to add it.
10x + 7y = 9
-4x - 7y = 9
See that 7y? You can cancel those out because one is negative, and one is positive. So those are gone. You finish adding the rest of the numbers as usual and solve for x.
6x = 18
x = 3
Take x, and plug it into either equation to find y.
10(3) + 7y = 9
7y = -21
y = -3
(3, -3)
Hope this helped!
