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A. Completethetwo-column proofofthe midline theorem. Choose the corresponding letter of your answer from the box on the right. Given: In ABAC, D is the midpoint of AB and E is the midpoint of AC. 2E 3. Prove: DE || BC, DE = - BC Statement Reason a) DA = FC b) Property of parallelogram c) Vertical Angles Theorem d) Definition of a parallelogram e) Substitution f) Segment Addition Postulate g) ABAC, D is the midpoint of AB and E is the midpoint of AC. h) If alternate interior angles are congruent, then lines are parallel. i) Definition of midpoint j) AADE = AFCE (1) Given (2) In a ray, point at a given distance from the endpoint of the ray. (3) (4) SAS Postulate EF = DE AE = CE 22= 23 (5) Z1= 4 AB || CF (8) (9) DB = CF Quadrilateral BDFC is a parallelogram. (6) (7) Definition of midpoint CPCTC (10) (11) k) DE = BC 1) Point-Plotting Theorem m) 2DE = DF DE is on the side of DF of parallelogram BDFC. (13) (14) Substitution (16) Substitution Substitution (12) %3D DE+EF DF DE + DE = DE (15) BC = DF (17) (18) n) СРСТС o) DE || BC p) Transitive property q) 2DE - BC r) DE BC !!

A. Completethetwo-column proofofthe midline theorem. Choose the corresponding letter of your answer from the box on the right. Given: In ABAC, D is the midpoint of AB and E is the midpoint of AC. 2E 3. Prove: DE || BC, DE = - BC Statement Reason a) DA = FC b) Property of parallelogram c) Vertical Angles Theorem d) Definition of a parallelogram e) Substitution f) Segment Addition Postulate g) ABAC, D is the midpoint of AB and E is the midpoint of AC. h) If alternate interior angles are congruent, then lines are parallel. i) Definition of midpoint j) AADE = AFCE (1) Given (2) In a ray, point at a given distance from the endpoint of the ray. (3) (4) SAS Postulate EF = DE AE = CE 22= 23 (5) Z1= 4 AB || CF (8) (9) DB = CF Quadrilateral BDFC is a parallelogram. (6) (7) Definition of midpoint CPCTC (10) (11) k) DE = BC 1) Point-Plotting Theorem m) 2DE = DF DE is on the side of DF of parallelogram BDFC. (13) (14) Substitution (16) Substitution Substitution (12) %3D DE+EF DF DE + DE = DE (15) BC = DF (17) (18) n) СРСТС o) DE || BC p) Transitive property q) 2DE - BC r) DE BC !!

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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A. Completethetwo-column proofofthe midline theorem. Choose the corresponding letter of your answer from the box on the right. Given: In ABAC, D is the midpoint of AB and E is the midpoint of AC. Prove: DE || BC, DE = - BC 2E 3 Statement Reason a) DA = FC b) Property of parallelogram c) Vertical Angles Theorem d) Definition of a parallelogram e) Substitution f) Segment Addition Postulate g) ABAC, D is the midpoint of AB and E is the midpoint of AC. h) If alternate interior angles are congruent, then lines are parallel. i) Definition of midpoint j) AADE = AFCE (1) Given (2) In a ray, point at a given distance from the endpoint of the ray. (3) (4) EF = DE AE = CE 22= 43 SAS Postulate (5) Z1= 4 AB || CF (8) (9) DB = CF (6) (7) Definition of midpoint СРСТС (10) Quadrilateral BDFC is a parallelogram. (11) k) DE = BC DE is on the side of DF of parallelogram BDFC. (13) (14) Substitution (16) Substitution Substitution 1) Point-Plotting Theorem m) 2DE = DF n) СРСТС o) DE || BC p) Transitive property q) 2DE - BC r) DE = BC (12) DE+EF DF DE + DE = DF (15) BC DF (17) L(18)
Transcribed Image Text:A. Completethetwo-column proofofthe midline theorem. Choose the corresponding letter of your answer from the box on the right. Given: In ABAC, D is the midpoint of AB and E is the midpoint of AC. Prove: DE || BC, DE = - BC 2E 3 Statement Reason a) DA = FC b) Property of parallelogram c) Vertical Angles Theorem d) Definition of a parallelogram e) Substitution f) Segment Addition Postulate g) ABAC, D is the midpoint of AB and E is the midpoint of AC. h) If alternate interior angles are congruent, then lines are parallel. i) Definition of midpoint j) AADE = AFCE (1) Given (2) In a ray, point at a given distance from the endpoint of the ray. (3) (4) EF = DE AE = CE 22= 43 SAS Postulate (5) Z1= 4 AB || CF (8) (9) DB = CF (6) (7) Definition of midpoint СРСТС (10) Quadrilateral BDFC is a parallelogram. (11) k) DE = BC DE is on the side of DF of parallelogram BDFC. (13) (14) Substitution (16) Substitution Substitution 1) Point-Plotting Theorem m) 2DE = DF n) СРСТС o) DE || BC p) Transitive property q) 2DE - BC r) DE = BC (12) DE+EF DF DE + DE = DF (15) BC DF (17) L(18)
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