Directions: Complete the following proof by adding the missing statement or reason. Use the choices inside the box below. Given: ACAN and ALYT; CA = LY, AN YT, LA > LYProve: CN > LTProof:Construct AW such that:• AW = AN = YT.__• Aw is between AC and AN, and• ZCAW LLYT.1.AConsequently, ACAW ALYT by SAS Triangle Congruence Postulate. So, CWLT because corresponding parts of congruent triangles are congruent.Construct the bisector AH of 4NAW such that:• H is on CN• ZNAH = LWAH2Consequently, ANAH = AWAH by SAS Triangle Congruence Postulate becauseAH = AH by reflexive property of equality and AW E AN from construction no. 1. So,WH = HN because corresponding parts of congruent triangles are congruent.StatementsReasonsFrom the illustration:CN = CH + HN1.1.2.CN CH + WH2.3.In ACHW, CH + WH> CW3.4.Using statement 2 in 3:4.CN > CWUsing statement in construction 1 in 5statement 4: CN> LT5.A. Triangle Equality theorem 3B. Segment addition PostulateC. Substitution property of equality (using statement 2 in 3)D. Substitution property of EqualityE. Substitution property of equality (using statement in construction 1 in statement 4)

To give reasons for the given statements.

AH = AH Dy reflexive property WH = HN because corresponding parts of congruent triangles are congruent. equality om construction hồ. 1. Số, Statements From the illustration: CN = CH + HN Reasons 1. 1. 2. CN = CH + WH 2. 3. In ACHW, CH + WH > CW 3. Using statement 2 in 3: CN > CW 4. 4. Using statement in construction 1 in5 statement 4: CN> LT 5. A. Triangle Equality theorem 3 B. Segment addition Postulate C. Substitution property of equality (using statement 2 in 3) D. Substitution property of Equality E. Substitution property of equality (using statement in construction 1 in statement 4)

AH = AH Dy reflexive property WH = HN because corresponding parts of congruent triangles are congruent. equality om construction hồ. 1. Số, Statements From the illustration: CN = CH + HN Reasons 1. 1. 2. CN = CH + WH 2. 3. In ACHW, CH + WH > CW 3. Using statement 2 in 3: CN > CW 4. 4. Using statement in construction 1 in5 statement 4: CN> LT 5. A. Triangle Equality theorem 3 B. Segment addition Postulate C. Substitution property of equality (using statement 2 in 3) D. Substitution property of Equality E. Substitution property of equality (using statement in construction 1 in statement 4)

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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Concept explainers

Angles

In mathematics, angles constitute a very important part. Just like the concept of lines, an angle is a necessary figure that is used for measurement. How do you define its formation? It is formed when two or more lines meet at a point. The point at which two or more lines meet is known as the vertex. When the lines get inclined at this point, they do form various angles. Angles are measured from the vertex in terms of degrees.

Question

100%

Directions: Complete the following proof by adding the missing statement or reason. Use the choices inside the box below.

Given: ACAN and ALYT; CA = LY, AN YT, LA > LY
Prove: CN > LT
Proof:
Construct AW such that:
• AW = AN = YT.__
• Aw is between AC and AN, and
• ZCAW LLYT.
1.
A
Consequently, ACAW ALYT by SAS Triangle Congruence Postulate. So, CW
LT because corresponding parts of congruent triangles are congruent.
Construct the bisector AH of 4NAW such that:
• H is on CN
• ZNAH = LWAH
2
Consequently, ANAH = AWAH by SAS Triangle Congruence Postulate because
AH = AH by reflexive property of equality and AW E AN from construction no. 1. So,
WH = HN because corresponding parts of congruent triangles are congruent.
Statements
Reasons
From the illustration:
CN = CH + HN
1.
1.
2.
CN CH + WH
2.
3.
In ACHW, CH + WH> CW
3.
4.
Using statement 2 in 3:
4.
CN > CW
Using statement in construction 1 in 5
statement 4: CN> LT
5.
A. Triangle Equality theorem 3
B. Segment addition Postulate
C. Substitution property of equality (using statement 2 in 3)
D. Substitution property of Equality
E. Substitution property of equality (using statement in construction 1 in statement 4)

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