MATHEMATICS MIDDLE SCHOOL

Given: ∠1 ≅ ∠2Prove: a ∥ b

What is the missing statement in the proof?

∠1 ≅ ∠2

a ⊥ b

a ∥ b

∠1 ≅ ∠4

Answers

Answer 1

Answer:

The missing statement in the proof is ∠1 ≅ ∠4.

Solution:

(1) Given ∠1 ≅ ∠2

(2) ∠1 and ∠4 are vertical angles.

Vertical angle theorem:

If two angles are vertically opposite then they are congruent.

By vertical angle theorem,

⇒ ∠1 ≅ ∠4

(3) Transitive property of congruence:

If A = B and B = C, then A = C.

From (1) and (2), ∠2 ≅ ∠4.

(4) If two lines and a transversal form congruent corresponding angles, then the lines are parallel.

Therefore line a || line b.

⇒ a || b.

Hence the missing statement in the proof is ∠1 ≅ ∠4.

Related Questions

Photo above. please help!
What is 9/6 in the equivalent fraction and as a percent
If the perimeter of an equilateral triangle is 60 cm, then what is its area?
A large chocolate bar has a base area of 47.1 square feet and it’s length is 0.7 feet longer than twice it’s width. Find the length and the width of the bar
Point B is the midpoint of Line segment A C . Horizontal line with points A, B, and C. A vertical line extends from point B through point D to create two right angles.Which statements about the figure must be true? Select three options.AngleDBC is bisected by ray BD.AngleABC is bisected by ray BD.BC = One-halfACLine segment D B is-congruent-to Line segment B C 2mAngleDBC = mAngleABC

What is 4/5+11/12= ?

Answers

To add the denominators have to be the same so the common denominator is 60. So your answer is 4•12=48 and 11•5=55 so 48+55=106 and when you divide that by 60 you get 1.716

Answer:

4/5+11/12= 1 43/60

Is it possible for two numbers to have a difference of 6, and also a sum of 6?

Answers

Answer:

yes

Step-by-step explanation:

sum:

• `x+y=6`

• `y=6-x`

Difference:

• `y-x=6`

• `y=x+6`

Answer:

yes 12-6 has a difference of 6 and a sum of 6

Step-by-step explanation:

Is 90×58. . .5,220 just making sure

Answers

Hey, Fractionscompar!
You are correct!
90*58=5220!
You can check this by doing 5220/90 and you should get 58.
I hope this helps;)

There are 8 boys and 7 girls and 195 in All

Answers

then there are 210 people since 8+7+195 = 210

Noah had 3 boxes of marbles. Each box has 34 marbles. Noah gave Michelle 9 marbles from each box. How many marbles does Noah have now? Who has the most marbles,Noah or Michelle please help and good luck

Answers

Noah has 75 marbles. Noah has more marbles. this is because 34 times 3 is equal to 102. since michelle takes 9 marbles from EACH box, 9 times 3 is 27. 102 minus 27 is 75

Question 51 pts
If one inch represents 14 feet, how many inches would you use to make a scale
drawing of a building that is 119 feet?
O 5 inches
O 8.5 inches
0 15 inches
O 105 inches