Mathematics, 30.03.2022 21:50 joydivision01
Look at the right triangle ABC:
Right triangle ABC has a right angle at B. Segment BD meets segment AC at a right angle.
A student made the following chart to prove that AB2 + BC2 = AC2:
Statement Justification
1. Triangle ABC is similar to triangle BDC 1. Angle ABC = Angle BDC and Angle BCA = Angle BCD
2. BC2 = AC ⋅ DC 2. BC ÷ DC = AC ÷ BC because triangle ABC is similar to triangle BDC
3. Triangle ABC is similar to triangle ABD 3. Angle ABC = Angle BAD and Angle BAC = Angle ABD
4. AB2 = AC ⋅ AD 4. AB ÷ AD = AC ÷ AB because triangle ABC is similar to triangle ADB
5. AB2 + BC2 = AC ⋅ AD + AC • DC = AC (AD + DC) 5. Adding Statement 1 and Statement 2
6. AB2 + BC2 = AC2 6. AD + DC = AC
Which justification is incorrect?
Justification 4
Justification 1
Justification 2
Justification 3
Answers: 1
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