In ΔABC shown below, BD over BA equals BE over BC: Triangle ABC with segment DE intersecting sides AB and BC respectively. The f
ollowing 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
1 answer:
You might be interested in
<em>I am against people doing this.</em>
<em>I think it's wrong because for some reason scientists are permitted to do this but that is breaking the law. I hate how they do it because these are just innocent animals that did nothing wrong to us, our scientists just decide it's ok to go stick needles in them and put stuff on them. My biggest problem with this is that they don't care about the effects their products have on innocent animals and instead of fixing their mistake and just apply it to humans, they just keep on going like there's no tomorrow. Animals have done nothing wrong to these people and I think that it's wrong to do so. Also, I don't really think that this proves anything. An animal's skin and fur are different than a human's skin and hair so it would make no sense to test these things on them because it really is guaranteed to give an accurate answer. Animals differ from us in so many ways that you should be able to think that scientists wouldn't harm these lovely creatures, but instead, they do. Why do scientists hurt these animals? I don't want to live in a world with hurt animals, especially when some of them have World Records, like the Sea Otter.</em>
<em>-R3TR0 Z3R0</em>
