Match the reasons with the statements in the proof. given: m1 = m3 m2 = m3 prove: / | | m 1. m∠1 = m∠3 and m∠2 = m∠3 substitution 2. m∠1 = m∠2 definition of alternate interior angles 3. ∠1 and ∠2 are alternate interior angles if alternate interior angles are equal, 4. l||m then the lines are parallel. given

Given: and

To prove that:

1.          [Given]

Substitution property of equality says that:

If x = y, then x can be substituted in y, or y can be substituted in x.

2          [ By Substitution Property]

Alternate interior angles states that when two lines are crossed by transversal , a pair of angles on the inner sides of each of these two lines on the opposite sides of the transversal line.

3. and   are alternate interior angles  [By definition Alternate interior angle].

Alternating interior angles theorem states that if two parallel lines are intersected by third lines, then the angles in the inner sides of the parallel lines on the opposite sides of the transversal are equal.

4. ; then the lines are parallel     [By Alternate interior angles theorem]

Correct match is as follows:

1.          [Given]

2.          [Substitution]

3. and   are alternate interior angle       [By definition of alternate interior angles ]

4. the lines are parallel  [If alternate interior angles are equal]

if im undersanding the question correctly, its organized from 10

step-by-step explanation:

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it