Question

Just need to be cheeked **proof**
Given:∠4≅∠5 Prove:m∠2+m∠3=90 deg.
Statements Reasons
1)∠4≅∠5 1)Given
2)a|b 2)Theroem 3.8
3)∠2 and∠3 3)Theroem3.9
are complemtray
4)m∠2+m∠3=90 deg 4) definition of a right angle

Answer 1

i have to find stamen 3 and reasons 2,3,and 4
theorem 3.8-if two lines intersect to form a linear pair congruent angles, then the lines are perpendicular
theorem3.9-if two lindes are perpendicular, then they intersect to form a right angles

Answer 2

@jim_thompson5910

Answer 3

reason 2 looks good, but thinking of an alternative to reason 3

Answer 4

theorem 3.10-if two sides of two adjacent acute angles are perpendicular then the angles are complemtary

Answer 5

that might be a better theorem, what other theorems do you have?

Answer 6

theorem 3.11-if a transversal is perpendicular to one of two parallel lines, then it is perrpendicular to the other

Answer 7

what I would do is this

Answer 8

angles 4 and 5 are congruent (given)

angles 4 and 5 are a linear pair (given)

so because of the two given statements above, we know that angles 4 and 5 are right angles

angles 2 and 3 combine to form a larger angle that's vertical to angle 5, so

angle 2 + angle 3 = angle 5

angle 2 + angle 3 = 90


that's the basic outline of how I would do it

Answer 9

Thanks:)

Answer 10

yw