1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ioda
3 years ago
15

Since ABCD is a parallelogram, the two pairs of _________ 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 _________, 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.
Mathematics
1 answer:
Marysya12 [62]3 years ago
7 0

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.

You might be interested in
Find the product. (-4·3·2)2 -48 48 -576 576
VLD [36.1K]
(-4*3*2)^2 = (-24)^2 = 576

hope this will help you 
5 0
3 years ago
Read 2 more answers
Michelle has 3
anyanavicka [17]

Answer: 4/5

Step-by-step explanation:

3 0
2 years ago
Can someone pls help me
noname [10]

Answer: Hewo, there! your Answer is Below

18.2 Would be your answer rounded to the nearest tent the Orignal Answer was 18.24

Step-by-step explanation:

Hope this Helps you!!!

Have a great day!!!

3 0
2 years ago
Ayuda porfa, quien entiende???
aksik [14]

Answer:

c

Step-by-step explanation:

the right answer is c it good

6 0
2 years ago
Question 20 of 40
frozen [14]

Answer:

A

Step-by-step explanation:

I guessed also I just took the exam

4 0
3 years ago
Other questions:
  • What is the mean of 23,25,24,26,23,25,22,22,23,40
    14·2 answers
  • What is the radius of a circle with a sector area of 7 (pi) sq ft. and an arc whose measure is 70°?
    9·1 answer
  • Ken went to the store for his mother. He spent $2.37 on groceries. In addition, his mother said he could spend $0.35 on candy. W
    13·2 answers
  • Solve 6^(4x+1)=5^(x-3) for x
    13·2 answers
  • Idk how to do this. Someone please help. This is a Geometry Honors class
    5·2 answers
  • My office is 11 feet wide and 13 feet long with the ceiling being 8 feet above the floor. I would like to paint the walls light
    7·1 answer
  • Triangle+ Triangle + Triangle = 30 Triangle + circle + circle = 20 Circle + Square + Square = 13 Triangle + circle x half square
    13·1 answer
  • Per year. How much interest will she be paid in the first
    9·1 answer
  • Your bank account balance is −$52.85. You deposit $65.50. What is your new balance?
    8·2 answers
  • PLEASE HELP ASAP JUST CLASSIFY THE TRIANGLE NOTHING ELSE​
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!