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
Kazeer [188]
2 years ago
7

Can someone help me with this please

Mathematics
1 answer:
Bingel [31]2 years ago
6 0

Answer:

  A.1: ∠BAC ≅ ∠BDC ≅ ∠EDF, ∠ACD ≅ ∠ABD ≅ ∠BDE ≅ ∠CDF

  A.2: ∠1 ≅ ∠4, ∠2 ≅ ∠3 ≅ ∠5 ≅ ∠6

  A.3: ∠2 ≅ ∠3

  B.1: ∠ACD ≅ ∠CAB, ∠CDA ≅ ∠ABC, ∠DAC ≅ ∠BCA

  B.2: ∠1 ≅ ∠3 ≅ ∠5, ∠2 ≅ ∠4 ≅ ∠6

  see "additional comment" regarding listing pairs

Step-by-step explanation:

There are a number of ways angles can be identified as congruent. In each case, the converse of the proposition is also true.

  • opposite angles of a parallelogram are congruent
  • corresponding angles where a transversal crosses parallel lines are congruent
  • alternate interior angles where a transversal crosses parallel lines are congruent
  • vertical angles are congruent
  • any two angles with the same measure are congruent

In these exercises, pairs of angles need to be examined to see which of these relations may apply.

__

<h3>A</h3>

<u>Left</u>

ABCD is a parallelogram, so the congruent angles are opposite angles and any that are vertical or corresponding:

  ∠BAC ≅ ∠BDC ≅ ∠EDF ≅ 110° (3 pairs)

  ∠ACD ≅ ∠ABD ≅ ∠BDE ≅ ∠CDF ≅ 70° (6 pairs)

<u>Center</u>

  ∠1 ≅ ∠4 ≅ 66° (1 pair) . . . . vertical angles

  ∠2 ≅ ∠3 ≅ ∠5 ≅ ∠6 ≅ 57° (6 pairs) . . . . marked with the same measure, and their vertical angles

<u>Right</u>

Assuming that lines appearing to go in the same direction actually do go in the same direction, the only pair of congruent angles in the figure is ...

  ∠2 ≅ ∠3

__

<h3>B</h3>

<u>Left</u>

Corresponding angles in congruent triangles are congruent. Here, the congruent triangles are ΔACD ≅ ΔCAB. So, the pairs of congruent angles are ...

  ∠ACD ≅ ∠CAB (30°)

  ∠CDA ≅ ∠ABC (90°)

  ∠DAC ≅ ∠BCA (60°)

<u>Right</u>

The corresponding angles and any vertical angles are congruent. This means all the odd-numbered angles in the figure are congruent, and all the even-numbered angles in the figure are congruent. The marked 72° angles show the "horizontal" segments are parallel by the converse of the corresponding angles theorem.

  ∠1 ≅ ∠3 ≅ ∠5 (72°) (3 pairs)

  ∠2 ≅ ∠4 ≅ ∠6 (108°) (3 pairs)

_____

<em>Additional comment</em>

The question asks you to list pairs of congruent angles. When 3 things are congruent, they can be arranged in 3 pairs:

  a ≅ b ≅ c   ⇒   (a≅b), (a≅c), (b≅c)

Similarly, when 4 things are congruent, they can be arranged in 6 pairs:

  a ≅ b ≅ c ≅ d   ⇒   (a≅b), (a≅c), (a≅d), (b≅c), (b≅d), (c≅d)

In the above, we have elected not to list all of the pairs, but to list the set of congruences from which pairs can be chosen.

You might be interested in
Plis only answer correctly
gregori [183]

Answer:

d

Step-by-step explanation:

d

dkimiunuhbubhwswdqwduoewdWEC W vcuuhdcosv

8 0
3 years ago
Read 2 more answers
Which of the following binomials is a factor of x^3+4x^2+x-6
larisa [96]
The answer could be 3, 2, or 1
5 0
3 years ago
(b) Three objects are brought close to each other, two at a time. When objects A and B are brought together, they repel. When ob
zheka24 [161]

Answer:

Step-by-step explanation:

When A and B are brought together then they repel i.e. A and B have same charge, either negative or positive

When B and C are brought together then they also repel. This implies that nature of charge on  B and C is same          

4 0
3 years ago
Find the slope.<br> (6,7) (2,-4)
emmainna [20.7K]
I'm pretty sure the slope is: - 4/11
7 0
3 years ago
Write one or two sentences to describe the cost function for the Wichita factory. (5 points)
Eva8 [605]
The answer would be -15      

this is my work

3*-6 to -18 (7-4-18)
4 0
3 years ago
Read 2 more answers
Other questions:
  • What is m∠A ?<br> Please see attachment <br> (The Triangle Sum Theorem)
    12·1 answer
  • Solve log8(x+2)-log8(x-1)=2/3
    12·1 answer
  • Marcie bought a 50-foot roll of packing tape.She used two 8 5/6 foot lengths.How much tape is left on the roll?
    8·2 answers
  • Which of the following is a true proportion
    8·2 answers
  • Find the difference.
    10·1 answer
  • 8 more than twice a number is equal to negitive 20
    11·2 answers
  • If 6% of the 205 million adult Americans are unemployed, how many adult Americans are unemployed?
    5·2 answers
  • Sarah began the week with $2.60 in her lunch account. She deposited $20 on Monday, and then spent $4.75 each day that week for l
    10·1 answer
  • GIVING OUT BRAINLIEST
    13·1 answer
  • What's the simplified expression of 6x2y3/2x−2?
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!