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nata0808 [166]
2 years ago
6

Fill in the blanks to complete this proof of theorem 2-3.

Mathematics
1 answer:
Basile [38]2 years ago
6 0

Answer:

Therefore.

angle 1 is congruent to angle 3 ...Proved

The proof with steps are below with Fill in the blanks

Step-by-step explanation:

Complementary Angles:

Two angles are Complementary when they add up to 90 degrees.

Example 40° and 50° are Complementary Angles.

If 'x' and 'y' are Complementary Angles the we have

x+y=90\°

Here,

Given:

angle 1 and angle 2 are complementary

angle 3 and angle 2 are complementary

To Prove:

angle 1 is congruent to angle 3

Proof:

Step 1:

angle 1 and angle 2 are complementary and angle 3 and angle 2 are complementary because it is Given.

Step 2:

By the definition of complementary angles,

m of angle 1 + m of angle 2 = _90°__ and m of angle 3 + m of angle 2 = _90°_.

Step 3:

Transitive Property of Equality.

Then m of angle 1 + m of angle 2 = m of angle 3 + m of angle 2 by the Transitive Property of Equality.

Step 4:

Subtract m of angle 2 from each side. By the Subtraction Property of Equality, you get

m\angle 1 +m\angle 2-m\angle 2=m\angle 3+m\angle 2-m\angle 2

m\angle 1=m\angle 3

m of angle 1 = _measure of angle_3_.

Step 5:

Angles with the same measure are _Congruent__,

Step 6:

so angle 1 is congruent to angle 3.

Therefore.

angle 1 is congruent to angle 3 ...Proved

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3 years ago
What additional info do you need
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Answer:

  ∠C ≅ ∠M  or  ∠B ≅ ∠L

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You are given an angle and its opposite side as being congruent. AAS requires two congruent angles and one side, so you need another set of congruent angles (one in each triangle). It does not matter which they are. The above-listed pairs are appropriate.*

_____

* Since the figure cannot be assumed to be drawn to scale, either of angles B or C could be declared congruent to either of angles L or M. However, it appears that angles B and L are opposite the longest side of the triangle, so it makes good sense to declare that pair congruent. The same congruence statement (ΔBCD≅ΔLMN) would result from declaring angles C and M congruent. So, either declaration will work (matches the last answer choice.)

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Corrected Question

Sue travels by bus or walks when she visits the shops. The probability that she catches the bus to the shops is 0.4. The probability she catches the bus from the shops is 0.7. Show the probability that Sue walks at one way is 0.72

Answer:

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Step-by-step explanation:

Sue travels by bus or walks when she visits the shops.

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Let the event that she catches the bus from the shop=B

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