subject
Mathematics, 14.07.2020 22:01 kaydeemyylady

Consider the diagram and the paragraph proof below. Given: Right △ABC as shown where CD is an altitude of the triangle Prove: a2 + b2 = c2 Triangle A B C is shown. Angle A C B is a right angle. An altitude is drawn from point C to point D on side A B to form a right angle. The length of C B is a, the length of A C is b, the length of A B is c, the length of A D is e, the length of D B is f, and the length of C D is h. Because △ABC and △CBD both have a right angle, and the same angle B is in both triangles, the triangles must be similar by AA. Likewise, △ABC and △ACD both have a right angle, and the same angle A is in both triangles, so they also must be similar by AA. The proportions StartFraction c Over a EndFraction = StartFraction a Over f EndFraction and StartFraction c Over b EndFraction = StartFraction b Over e EndFraction are true because they are ratios of corresponding parts of similar triangles. The two proportions can be rewritten as a2 = cf and b2 = ce. Adding b2 to both sides of first equation, a2 = cf, results in the equation a2 + b2 = cf + b2. Because b2 and ce are equal, ce can be substituted into the right side of the equation for b2, resulting in the equation a2 + b2 = cf + ce. Applying the converse of the distributive property results in the equation a2 + b2 = c(f + e). Which is the last sentence of the proof?

ansver
Answers: 3

Other questions on the subject: Mathematics

image
Mathematics, 21.06.2019 16:30, 2alshawe201
You are remodeling your kitchen. you’ve contacted two tiling companies who gladly told you how long it took their workers to tile of a similar size jim completed half the floor in 8 hours. pete completed half of the other floor in 7 hours. if pete can lay 20 more tiles per hour than jim, at what rate can jim lay tiles
Answers: 3
image
Mathematics, 21.06.2019 18:00, ash0470
Sara can take no more than 22 pounds of luggage on a trip. her suitcase weighs 112 ounces. how many more pounds can she pack without going over the limit?
Answers: 1
image
Mathematics, 21.06.2019 20:00, travisvb
Consider the set of all four-digit positive integers less than 2000 whose digits have a sum of 24. what is the median of this set of integers?
Answers: 1
image
Mathematics, 21.06.2019 21:00, hastephens03
Mr. thompson is on a diet. he currently weighs 260 pounds. he loses 4 pounds per month. what part of the story makes the relationship not proportional?
Answers: 3
You know the right answer?
Consider the diagram and the paragraph proof below. Given: Right △ABC as shown where CD is an altitu...

Questions in other subjects:

Konu
Mathematics, 23.11.2019 13:31