Question

prove corresponding angles are cong ruent​

Answer 1

Answer:

Suppose you have two parallel lines cut by a transversal.

Due to the straight angle (linear pair) theorem, we know that

{

m

∠

2

+

m

∠

3

=

180

˚

m

∠

5

+

m

∠

6

=

180

˚

Thought the transitive property, we can say that

m

∠

2

+

m

∠

3

=

m

∠

5

+

m

∠

6

×

×

(1)

Though the alternate interior angles theorem, we know that

m

∠

3

=

m

∠

5

Use substitution in (1):

m

∠

2

+

m

∠

3

=

m

∠

3

+

m

∠

6

Subtract

m

∠

3

from both sides of the equation

m

∠

2

=

m

∠

6

∴

∠

2

≅

∠

6

Thus

∠

2

and

∠

6

are corresponding angles and have proven to be congruent.

Answer 2

Explanation:

prove corresponding angles are cong ruent