Triangles Question

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For the following proof, choose the correct missing statement and reasons in the questions below.

In the following figure,

$bar{AB} " || " bar{CE}$ ,

$ang BFE$ and

$ang CDE$ are supplementary, and points

$A,F,E$ are collinear. Also,

$ang BCD ~= ang CDE$ and

$bar{AF} ~= bar{ED}$ . If

$BC = 2CD$ and

$CD = 2 ED$ , prove that

$BD*BF = AB*BC$ (

$bar{BD}$ is not drawn).

Trapezoid ABCDEF

$\ \ \ \ \ \ \ \ \ \ \ \ \mathbf{"Statement"} \ \ \ \ \ \ \ \ \ \ \ \$	$\mathbf{"Reason"}$
$1. ang BCD ~= ang CDE$	$1. "Given"$
$2. BC = 2CD$	$2. "Given"$
$3. (BC)/(CD) = 2$	$3. "Division Property of Equality"$
$4. CD = 2ED$	$4. "Given"$
$5. (CD)/(ED) = 2$	$5. "Division Property of Equality"$
$6. (BC)/(CD) = (CD)/(ED)$	$6. "Transitive Property of Equality"$
$7.$	$7. "SAS Similarity Theorem"$
$8. (BD)/(CE) = (BC)/(CD)$	$8. "Ratios corr. sides of similar triangles are equal"$
$9. bar{AF} ~= bar{ED}$	$9. "Given"$
$10. bar{AB} " \|\| " bar{CE}$	$10. "Given"$
$11. ang BAF ~= ang CED$	$11. ""$
$12. ang BFE " and " ang CDE " are supplementary"$	$12. "Given"$
$13. m ang BFE + m ang CDE = 180°$	$13. ""$
$14. m ang BFE = 180° - m ang CDE$	$14. "Subtraction Property of Equality"$
$15. A, F, E " are collinear"$	$15. "Given"$
$16. m ang AFB + m ang BFE = 180°$	$16. ""$
$17. m ang BFE = 180° - m ang AFB$	$17. "Subtraction Property of Equality"$
$18. 180° - m ang CDE = 180° - m ang ABF$	$18. "Transitive Property of Equality"$
$19. - m ang CDE = - m ang AFB$	$19. "Subtraction Property of Equality"$
$20. m ang CDE = m ang AFB$	$20. "Multiplication Property of Equality"$
$21. ang CDE ~= ang AFB$	$21. "Definition of Congruent Angles"$
$22. Delta AFB ~= Delta EDC$	$22. ""$
$23. bar{AB} ~= bar{CE}$	$23. "Corr. sides of congruent triangles congruent"$
$24. AB = CE$	$24. "Definition of Congruent Segments"$
$25. bar{BF} ~= bar{CD}$	$25. "Corr. sides of congruent triangles congruent"$
$26. BF = CD$	$26. "Definition of Congruent Segments"$
$27. (BD)/(CE) = (BC)/(CD)$	$27. "Earlier result"$
$28. (BD)/(AB) = (BC)/(BF)$	$28. "Substitution Property of Equality"$
$29. BDBF = ABBC$	$29. "Multiplication Property of Equality"$

Grade 10 Triangles CCSS: HSG-SRT.B.5

What is the missing statement in step 7?

$Delta BCD \ ~ \ Delta CDE$
$Delta BCD \ ~ \ Delta CED$
$Delta BCD \ ~ \ Delta DEC$
$Delta BCD \ ~ \ Delta DCE$

Question Info

Triangles Question

Grade 10 Triangles CCSS: HSG-SRT.B.5