Question

A conjecture and the paragraph proof used to prove the conjecture are shown.



Given: angle 1 is congruent to angle 4. Prove: angle 2 is congruent to angle 3. Two rays share an endpoint. Two similar rays opposite in direction share another end point just opposite to the previous endpoint. The obtuse angle made by the upper rays in outward direction is labeled 1. The obtuse angle made by the lower rays in outward direction is labeled 4. The obtuse angle made by the upper rays in inward direction is labeled 2. The obtuse angle made by the upper rays in inward direction is labeled 3.


Drag an expression or statement to each box to complete the proof.

It is given that ∠1≅ ∠4 ​. By the vertical angle theorem, ≅∠1 . Therefore, ∠2≅∠4 by the substitution property. By the , ∠4≅∠3 . So, ∠2≅ by the .

Answer 1

Answer:

Drawn two rays l and m whose end point i.e at the point they meet is C.

Inner obtuse angle =∠2

Outer obtuse angle =∠1

Now, another two rays meet at point D, rays being p and q.

Inner obtuse angle =∠3

Outer obtuse angle = ∠4

as ∠1 + ∠ 2=360°.............(1)

and, ∠ 3+ ∠4=360°...............(2)

from (1) and (2)

∠1+∠2=∠3+∠4

But, ∠ 1≅∠4 [Given]

So , ∠3 = ∠ 4 [ by substitution property]

Answer 2

Answer:

It is given that <1 = <4. By the vertical angle theorem, *<4* = <1. Therefore, <2 = <4 by the substitution property. By the *transitive property of congruence*, <4 = <3. So, <2 = *<3* by the *vertical angle theorem*.

Step-by-step explanation:

I just used what makes sense to me, haven't turned my test in yet but I am 99% this is correct. better than the other answer at least.