In the triangle shown, BC is parallel to DE. E B A two-column proof is provided to prove that DE divides BA and CA proportionally. Step Statement Reason 1 BC is parallel to DE: Given 2 ZBAC E ZDAE ? 3 ZABC 2 LADE Corresponding angles are congruent. 4 ABAC - ADAE Angle-Angle (AA) Similarity Corresponding sides of similar triangles are proportional. ? AD + DB = AB 6 Segment Addition Postulate AE + EC = AC AD + DB AE + EC 7 Substitution AD AE DB ЕС 8 Subtraction Property of Equality AD AE 5

In the triangle shown, BC is parallel to DE. E B A two-column proof is provided to prove that DE divides BA and CA proportionally. Step Statement Reason 1 BC is parallel to DE: Given 2 ZBAC E ZDAE ? 3 ZABC 2 LADE Corresponding angles are congruent. 4 ABAC - ADAE Angle-Angle (AA) Similarity Corresponding sides of similar triangles are proportional. ? AD + DB = AB 6 Segment Addition Postulate AE + EC = AC AD + DB AE + EC 7 Substitution AD AE DB ЕС 8 Subtraction Property of Equality AD AE 5

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

There are 2 parts, The first question with the choices should be the letter for step 2 under reasons and the 2nd question should be the answer for step 5 under statements

In the triangle shown, BC is parallel to DE.
В
A two-column proof is provided to prove that DE divides BA and CA proportionally.
Step
Statement
Reason
1
BC is parallel to DE:
Given
ZBAC E ZDAE
?
3
ZABC 2 LADE
Corresponding angles are congruent.
4
ABAC - ADAE
Angle-Angle (AA) Similarity
Corresponding sides of similar triangles
are proportional.
?
AD + DB = AB
Segment Addition Postulate
AE + EC = AC
AD + DB
AE + EC
7
Substitution
AD
AE
DB
EC
8
Subtraction Property of Equality
AD
AE
5

O A. Angle-Angle (AA) Similarity
O B. Reflexive Property of Congruence
O C. Vertical angles are congruent.
O D. Corresponding angles are congruent.
Activity 2 of 2
Part B: Which of the following statements should be given for Step 5?
O A. AD AC
AB
AE
о в АВ
AE
AD
AC
о с. АВ
AC
AD
AE
O D. AB
AC
AD
BC

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