Exercise 1 completela the tollowing proof. 1. Given: AB = CD₂AB BD, CD BD, E is the midpoint of BD. Prove AABE SACDE ar Proot: Statements 1. AB CD ABBD 1.LB is a right angle right angle 14.10 -5.LB=LD -6.5 is the midpoint of BD 7. 8. AABE = ACDE B Reasons DATE 7. Difinition of a ST C DUN 2. Definition of perpendicularity 3. Given MOLOHA A 4. Definition of Rerpendicularity S. D Midpoint ta 6 G F
Add an Answer
More Questions From This User See All
Answers & Comments
Here is a completed proof:
Statements Reasons
1. AB = CD Given
2. AB = BD Algebraic substitution
3. CD = BD Algebraic substitution
4. LB is a right angle Given
5. LB = LD Midpoint theorem
6. 5 is the midpoint of BD Given
7. AE = EB Midpoint theorem
8. AC = AD Pythagorean theorem
9. CE = DE Subtraction property of equality
10. AABE is a right triangle Definition of a right triangle
11. SACD is a right triangle Definition of a right triangle
12. AABE and SACD have a common side AB Given
13. AABE and SACD have a common side BD Given
14. . AE = CE Definition of midpoint
15. BE = DE Definition of midpoint
16. AABE = AC² + CB² Pythagorean theorem
17. SACD = SC² + CD² Pythagorean theorem
18. AC² + CB² = SC² + CD² Substitution using statements 1, 8, 9
19. AABE = SACD Substitution using statements 16, 17, 18
Therefore, AABE is congruent to SACD by the hypotenuse-leg congruence theorem (HL), since they have a common hypotenuse AB and the legs AE=CE and BE=DE are congruent by the midpoint theorem.
PA BRAINLLIEST PLEASE