subject
Mathematics, 30.11.2020 21:30 jonesnr10

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?

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

ansver
Answers: 3

Another question on Mathematics

question
Mathematics, 21.06.2019 17:30
Regular price 75$ discount 25%sale price?
Answers: 2
question
Mathematics, 21.06.2019 18:00
The base of a triangle exceeds the height by 7 centimeters. if the area is 400 square centimeters, find the length of the base and the height of the triangle.
Answers: 1
question
Mathematics, 21.06.2019 21:30
Consider the following equation. 1/2x^3+x-7=-3sqrtx-1 approximate the solution to the equation using three iterations of successive approximation. use the graph below as a starting point. a. b. c. d.
Answers: 3
question
Mathematics, 22.06.2019 00:50
Randy and trey take turns cleaning offices on the weekends. it takes randy at most 4 hours to clean the offices. it takes trey at most 6 hours to clean the offices. what is the greatest amount of time it would take them to clean the offices together? 2.4 hours 2.5 hours
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
Advanced Placement (AP), 07.03.2020 01:21