Question

Given: ΔABC Prove: The sum of the interior angle measures of ΔABC is 180°. Statement Reason 1. Let points A, B, and C form a triangle. Given 2. Let be a line passing through B, parallel to , with angles as labeled. Defining a parallel line and labeling angles 3. 4. M∠1 = m∠4, and m∠3 = m∠5. Congruent angles have equal measures. 5. M∠4 + m∠2 + m∠5 = 180° angle addition and definition of a straight angle 6. M∠1 + m∠2 + m∠3 = 180° substitution What is the missing step in this proof? A. Statement: ∠4 ≅ ∠5, and ∠1 ≅ ∠3. Reason: Alternate Interior Angles Theorem B. Statement: is parallel to. Reason: is a transversal cutting and. C. Statement: ∠1 ≅ ∠4, and ∠3 ≅ ∠5. Reason: Alternate Interior Angles Theorem D. Statement: ∠1 ≅ ∠4, and ∠3 ≅ ∠5. Reason: ∠1 and ∠4, and ∠3 and ∠5 are pairs of supplementary angles

Answer 1

From the given statements regarding angle the point b) DE is parallel to AC with its reason - AB is a transversal cutting DE and AC will be the correct statement.

DE and AC are parallel for this to work angle 1 is at A, angle 2 is at B and angle 3 is at C. In addition, angle 4 is the alternate interior angle to angle 1 once DE is constructed, as is angle 5 to angle 3. Then the missing reasons are alternate interior angles theorem and definition of congruent angles.

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