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nata0808 [166]
3 years ago
6

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

Mathematics
1 answer:
Basile [38]3 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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a chess player played 136 games total. If he won 56 of the games, what is the ratio of games he lost to games he won?​
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A square has an area of 576 square inches. How long is each side in feet?
Maru [420]
The area of this square is said to be 576 square inches.
The formula for the area of a square is the length of one side squared.
Let's use l to represent the side length.
This means l^2 = 576.
To find l, find the square root of both sides.
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</span>
The length of each side of the square is 24 inches.
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3 years ago
There are total of 84 students in the robotics club and the science club. The science club has 12 more students than the robotic
kari74 [83]
First off we have x number of students in the robotics club, 12 more in the Science club, and 84 students in total. This means:
Robotics Club = x
Science Club = (x + 12)
Total = 84

Okay, so here's the equation:

x + (x + 12) = 84 ~ Add like terms.
2x + 12 = 84 ~ Subtract 12 by both sides.
2x = 72 ~ Divide both sides by 2.
x = 36 ~ Meaning that the Robotics Club has 36 members.

At this point you can do: 84 - 36 = 48 which gives you the number of members in the Science Club, though...:

36 + (36 + 12) = 84 ~ Add the two in the parenthesis to get your answer.
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In conclusion: The Science Club has 48 students.

Hope that helps. ^ ^
{-Ghostgate-}
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3 years ago
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