subject
Mathematics, 07.12.2021 03:30 GreenHerbz206

In ΔABC shown below, BD over BA equals BE over BC: Triangle ABC with segment DE intersecting sides AB and BC respectively.

The following flowchart proof with missing statements and reasons proves that if a line intersects two sides of a triangle and divides these sides proportionally, the line is parallel to the third side:

Top path, by Given the ratio of line segments BD to BA is equal to the ratio of line segments BE to BC. By Side Angle Side Similarity Postulate, triangle ABC is similar to triangle DBE. By Corresponding Parts of Similar Triangles, angle BDE is congruent to angle BAC. By Converse of the Corresponding Angles Postulate, line segment DE is parallel to line segment AC. Bottom path, by space labeled as 2, space labeled by 1 occurs. By Side Angle Side Similarity Postulate, triangle ABC is similar to triangle DBE. By Corresponding Parts of Similar Triangles, angle BDE is congruent to angle BAC. By Converse of the Corresponding Angles Postulate, line segment DE is parallel to line segment AC.

Which reason can be used to fill in the numbered blank space?

Group of answer choices

1. ∠A ≅ ∠A
2. Reflexive Property of Equality

1. ∠A ≅ ∠B
2. Corresponding Parts of Similar Triangles

1. ∠A ≅ ∠B
2. Corresponding Angles Postulate

1. ∠B ≅ ∠B
2. Reflexive Property of Equality


In ΔABC shown below, BD over BA equals BE over BC:

Triangle ABC with segment DE intersecting side

ansver
Answers: 3

Another question on Mathematics

question
Mathematics, 21.06.2019 19:00
Simplify. −4x^2 (5x^4−3x^2+x−2) −20x^6−12x^4+8x^3−8x^2 −20x^6+12x^4−4x^3+8x^2 −20x^8+12x^4−4x^2+8x −20x^6+12x^4+4x^3−8x^2
Answers: 1
question
Mathematics, 21.06.2019 21:00
Select the correct answer from each drop-down menu. a system of equations and its solution are given below. system a complete the sentences to explain what steps were followed to obtain the system of equations below. system b to get system b, the equation in system a was replaced by the sum of that equation and times the equation. the solution to system b the same as the solution to system a.]
Answers: 1
question
Mathematics, 21.06.2019 21:50
What is the next step in the given proof? choose the most logical approach. a. statement: m 1 + m 2 + 2(m 3) = 180° reason: angle addition b. statement: m 1 + m 3 = m 2 + m 3 reason: transitive property of equality c. statement: m 1 = m 2 reason: subtraction property of equality d. statement: m 1 + m 2 = m 2 + m 3 reason: substitution property of equality e. statement: 2(m 1) = m 2 + m 3 reason: substitution property of equality
Answers: 3
question
Mathematics, 21.06.2019 23:30
Johnny rode his bike to a friends house 4 blocks down the street in his neighborhood. he immediately rode back home once he realized his friend was unable to play. what was his displacement for the total bike ride trip? what could you use as a reference point ? show the steps to solve this problem.
Answers: 3
You know the right answer?
In ΔABC shown below, BD over BA equals BE over BC: Triangle ABC with segment DE intersecting sides...
Questions
question
Mathematics, 11.04.2020 01:33
question
English, 11.04.2020 01:33
question
Mathematics, 11.04.2020 01:33