Below is a two-column proof incorrectly proving that the three angles of ?PQR sum to 180: Statements Reasons ?QRY ? ?PQRAlternate Interior Angles Theorem Draw line ZY parallel to segment PQ Construction m?ZRP + m?PRQ + m?QRY = m?ZRY Angle Addition Postulate ?ZRP ? ?RPQ Alternate Interior Angles Theorem m?RPQ + m?PRQ + m?PQR = m?ZRY Substitution m?ZRY = 180 Definition of a Straight Angle m?RPQ + m?PRQ + m?PQR = 180 Substitution Which statement will accurately correct the two-column proof?

A.) The measure of angle ZRY equals 180 by definition of supplementary angles.

B.) Angles QRY and PQR should be proven congruent after the construction of line ZY.

C.) The three angles of ?PQR equal 180 according to the Transitive Property of Equality.

D.) Line ZY should be drawn parallel to segment QR.

Question

11-02-2020
Mathematics

contestada

Below is a two-column proof incorrectly proving that the three angles of ?PQR sum to 180: Statements Reasons ?QRY ? ?PQRAlternate Interior Angles Theorem Draw line ZY parallel to segment PQ Construction m?ZRP + m?PRQ + m?QRY = m?ZRY Angle Addition Postulate ?ZRP ? ?RPQ Alternate Interior Angles Theorem m?RPQ + m?PRQ + m?PQR = m?ZRY Substitution m?ZRY = 180 Definition of a Straight Angle m?RPQ + m?PRQ + m?PQR = 180 Substitution Which statement will accurately correct the two-column proof?

A.) The measure of angle ZRY equals 180 by definition of supplementary angles.

B.) Angles QRY and PQR should be proven congruent after the construction of line ZY.

C.) The three angles of ?PQR equal 180 according to the Transitive Property of Equality.

D.) Line ZY should be drawn parallel to segment QR.

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MrRoyal MrRoyal · Answer 1 · 2021-08-11T10:13:22+02:00

The sum of angles in a triangle can be proven to equal 180 in quite a number of ways. The statement that accurately corrects the proof is:

(a) [tex]\angle ZRY = 180^o[/tex] by the definition of angle on a straight line.

I've added the image of the triangle and the straight line as an attachment.

From the attachment:

[tex]\angle QRY = \angle PQR[/tex] ---- alternate interior angles

Similarly

[tex]\angle ZRP = \angle RPQ[/tex] ---- alternate interior angles

So:

[tex]\angle ZRP + \angle QRY + \angle PRQ = 180^o[/tex] because [tex]\angle ZRP , \angle QRY , \angle PRQ[/tex] are all on a straight line, and the angles on a straight line add up to [tex]180^o[/tex].

Hence, the complete statement is: (a) [tex]\angle ZRY = 180^o[/tex] by the definition of angle on a straight line.