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

Other questions on the subject: Mathematics

image
Mathematics, 21.06.2019 14:00, lujaynsparkles
Which solid has two triangular bases and three lateral faces, each in the shape of a rectangle? triangular prism triangular pyramid rectangular prism rectangular pyramid
Answers: 3
image
Mathematics, 21.06.2019 17:30, Vampfox
Monthly water bills for a city have a mean of $108.43 and a standard deviation of $32.09. find the probability that a randomly selected bill will have an amount greater than $155, which the city believes might indicate that someone is wasting water. would a bill that size be considered unusual?
Answers: 1
image
Mathematics, 21.06.2019 18:00, kalibaby
Find the slope and the y-intercept if there's one and the equation of the line given these two points( 3, 2) and( 3, -4)
Answers: 2
image
Mathematics, 21.06.2019 20:40, ineedhelp773
Lines a and b are parallel. what is the value of x? -5 -10 -35 -55
Answers: 2
You know the right answer?
In ΔABC shown below, BD over BA equals BE over BC: Triangle ABC with segment DE intersecting sides...

Questions in other subjects: