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nika2105 [10]
3 years ago
11

When you start from a given set of rules and conditions and determine what must be true you are using _ reasoning

Mathematics
1 answer:
asambeis [7]3 years ago
4 0

Answer:

Deductive

Step-by-step explanation:

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Can someone help me with this please
Bingel [31]

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.

6 0
3 years ago
What is the value of w?
PilotLPTM [1.2K]
The Answer is-2.5 because first multiply the numbers are in parentheses
8 0
3 years ago
What is the solution to the equation 1/4x−3/4=1/2, given the replacement set {−1, 1, 5} ?
d1i1m1o1n [39]

Answer:

x=5

Step-by-step explanation:

I took the test. Hope this helps

6 0
3 years ago
|x-4|-3&lt;5 can someone help me
Alinara [238K]
|x - 4| - 3 < 5 \\ |x - 4| < 8 \\ - 8 < x - 4 < 8 \\ - 4 < x < 12
3 0
3 years ago
Value of 3v-7 given that 5v +9=4​
Y_Kistochka [10]

Answer:

The solution is -10

Step-by-step explanation:

We first solve for v in the equation;

5v + 9 = 4

5v = 4 - 9

5v = -5

v = -1

Finally, we substitute v = -1 in the given expression;

3v - 7

3(-1) - 7 = -10

8 0
3 years ago
Read 2 more answers
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