Similar and Congruent Figures Question

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Choose the correct missing statements and reasons in the questions below for the following proof.

Given right triangle

$Delta ABC$ , as seen below, with altitude

$bar{CD}$ , prove that

$AC^2 + BC^2 = AB^2$ .

Right Triangle ABCD

$\ \ \ \ \ \ \ \ \ \ \ \ \mathbf{"Statement"} \ \ \ \ \ \ \ \ \ \ \ \$	$\mathbf{"Reason"}$
$1. Delta ABC " is a right triangle"$	$1. "Given"$
$2. m ang A + m ang B = 90°$	$2. "Sum of acute angles in right triangle is 90°"$
$3. m ang A = 90° - m ang B$	$3. "Subtraction Property of Equality"$
$4. bar{CD} " is an altitude of " Delta ABC$	$4. "Given"$
$5. ang ADC " is a right angle"$	$5. "Definition of an altitude"$
$6. Delta ADC " is a right triangle"$	$6. ""$
$7. m ang A + m ang ACD = 90°$	$7. ""$
$8. m ang A = 90° - m ang ACD$	$8. "Subtraction Property of Equality"$
$9. 90° - m ang B = 90° - m ang ACD$	$9. ""$
$10. -m ang B = -m ang ACD$	$10. "Subtraction Property of Equality"$
$11. m ang B = m ang ACD$	$11. "Multiplication Property of Equality"$
$12. ang B ~= ang ACD$	$12. "Definition of congruent angles"$
$13. ang A ~= ang A$	$13. "Reflexive Property of Congruence"$
$14.$	$14. "AA Similarity Theorem"$
$15. bar{CD} " is an altitude of " Delta ABC$	$15. "Earlier result"$
$16. ang BDC " is a right angle"$	$16. "Definition of an altitude"$
$17. Delta BDC " is a right triangle"$	$17. "Definition of a right triangle"$
$18. m ang B + m ang BCD = 90°$	$18. ""$
$19. m ang B = 90° - m ang BCD$	$19. "Subtraction Property of Equality"$
$20. m ang A + m ang B = 90°$	$20. "Earlier result"$
$21.m ang B = 90° - m ang A$	$21. "Subtraction Property of Equality"$
$22. 90° - m ang BCD = 90° - m ang A$	$22. "Transitive Property of Equality"$
$23. - m ang BCD = - m ang A$	$23. "Subtraction Property of Equality"$
$24. m ang BCD = m ang A$	$24. "Multiplication Property of Equality"$
$25. ang BCD ~= ang A$	$25. "Definition of congruent angles"$
$26. ang B ~= ang B$	$26. "Reflexive Property of Congruence"$
$27.$	$27. "AA Similarity Theorem"$
$28.$	$28. "Ratios of corr. sides of sim. triangles equal"$
$29. BC^2 = AB * BD$	$29. "Multiplication Property of Equality"$
$30.$	$30. "Ratios of corr. sides of sim. triangles equal"$
$31. AC^2 = AB * AD$	$31. "Multiplication Property of Equality"$
$32. AB = AD+BD$	$32. ""$
$33. AB - BD = AD$	$33. "Subtraction Property of Equality"$
$34. AC^2 + BC^2 = ABAD + ABBD$	$34. ""$
$35. AC^2 + BC^2 = AB(AB - BD) + ABBD$	$35. "Substitution Property of Equality"$
$36. AC^2 + BC^2 = AB^2 - ABBD + ABBD$	$36. "Distribution Property of Equality"$
$37. AC^2 + BC^2 = AB^2$	$37. "Algebra (subtraction)"$

Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.4

What is the missing reason in step 9?

Addition Property of Equality
Transitive Property of Equality
Subtraction Property of Equality
Corresponding angles of congruent triangles are congruent

Question Info

Similar and Congruent Figures Question

Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.4