Question

Triangle Proofs Practice
Complete this assessment to review what you’ve learned. It will not count toward your grade.
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Question
Use the image to answer the question.

An illustration shows a triangle with angles marked as 1, 2 and 3, clockwise beginning at the top angle. A line is drawn outside of the triangle, passing through the vertex with angle 3.

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.

Answer 1

To complete the proof, you can fill in the blanks as follows:

Given the diagram shown, ∠ **3** ≅∠**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∠**1**+m∠**3**+m∠**4**=180° by the definition of a straight angle. Finally, m∠**1**+m∠**3**+m∠**2**=180° by substitution.

So the filled-in proof reads:

Given the diagram shown, ∠**3** ≅ ∠**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∠**1**+m∠**3**+m∠**4**=180° by the definition of a straight angle. Finally, m∠**1**+m∠**3**+m∠**2**=180° by substitution.