Fill in the blanks to complete the proof that m∠1+m∠3+m∠2=180°
given the diagram.
(2 points)
Given the diagram shown, ∠
≅∠5
; ∠2≅∠4
because alternate interior angles are congruent when lines are parallel. Then, I know that m∠1=m∠5
; m∠2=m∠4
because congruent angles have equal measures. m∠
+m∠3+m∠4=180°
by the definition of a straight angle. Finally, m∠1+m∠3+m∠
=180°
by substitution.
m∠1+m∠3+m∠2=180°.
To fill in the blanks and complete the proof, you have:
Given the diagram shown, ∠1 ≅ ∠5; ∠2 ≅ ∠4 because alternate interior angles are congruent when lines are parallel.
Then, I know that ∠1 = ∠5; ∠2 = ∠4 because congruent angles have equal measures.
So, we have:
m∠1 + m∠3 + m∠4 = 180° (by the definition of a straight angle)
Finally, m∠1 + m∠3 + m∠2 = 180° (by substitution)
Therefore, by filling in the given information, applying the properties of congruent angles and the definition of a straight angle, we have proven that m∠1 + m∠3 + m∠2 equals 180°.
To complete the proof, we can use the given information and the properties of congruent and parallel lines.
1. Given: ∠ ≅∠5; ∠2≅∠4 (Alternate interior angles are congruent when lines are parallel)
2. Therefore, we know that: m∠1=m∠5; m∠2=m∠4 (Congruent angles have equal measures)
3. By the definition of a straight angle, we know that: m∠ + m∠3 + m∠4=180°
4. Substituting the known values from step 2, we have: m∠1 + m∠3 + m∠4=180° (substitution)
Thus, we have proved that m∠1 + m∠3 + m∠2 = 180° using the given diagram and the properties of congruent and parallel lines.