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tester [92]
3 years ago
7

Given: ∠1 ≅ ∠2

Mathematics
1 answer:
Kitty [74]3 years ago
3 0

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

Solution:

(1)  Given ∠1 ≅ ∠2

(2) ∠1 and ∠4 are vertical angles.  

<u>Vertical angle theorem: </u>

If two angles are vertically opposite then they are congruent.

By vertical angle theorem,

⇒ ∠1 ≅ ∠4

(3) <u>Transitive property of congruence:</u>

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.

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