Quadrilaterals Question

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

Given that

$Delta AFB ~= Delta EDC$ ,

$bar{BC} " || " bar{FD}$ ,

$m ang BFE = 90°$ , and points

$A,F,E$ are collinear, prove that quadrilateral

$BCDF$ is a rectangle.

Trapezoid ABCDEF

$\ \ \ \ \ \ \ \ \ \ \ \ \mathbf{"Statement"} \ \ \ \ \ \ \ \ \ \ \ \$	$\mathbf{"Reason"}$
$1. m ang BFE = 90°$	$1. "Given"$
$2. A,F,E " are collinear"$	$2. "Given"$
$3. m ang AFB + m ang BFE = 180°$	$3. ""$
$4.$	$4. "Substitution Property of Equality"$
$5. m ang AFB = 180° - 90°$	$5. "Subtraction Property of Equality"$
$6. m ang AFB = 90°$	$6. "Algebra (subtract)"$
$7. Delta AFB ~= Delta EDC$	$7. "Given"$
$8.$	$8. "Corr. angles of congruent triangles congruent"$
$9. m ang AFB = m ang EDC$	$9. "Definition congruent angles"$
$10. 90° = m ang EDC$	$10. "Substitution Property of Equality"$
$11. bar{BC} " \|\| " bar{DF}$	$11. "Given"$
$12. m ang EDC + m ang BCD = 180°$	$12. ""$
$13. 90° + m ang BCD = 180°$	$13. "Substitution Property of Equality"$
$14. m ang BCD = 180° - 90°$	$14. "Subtraction Property of Equality"$
$15. m ang BCD = 90°$	$15. "Algebra (subtract)"$
$16. m ang BFE + m ang EDC + m ang BCD +$ $\ \ \ \ m ang CBF = 360°$	$16. ""$
$17. 90° + 90° + 90° + m ang CBF = 360°$	$17. "Substitution Property of Equality"$
$18. 270° + m ang CFB = 360°$	$18. "Algebra (add)"$
$19. m ang CFB = 360° - 270°$	$19. "Subtraction Property of Equality"$
$20. m ang CFB = 90°$	$20. "Algebra (subtract)"$
$21. ang BFE, \ ang EDC, \ ang BCD, \ ang CBF$ $\ \ \ " are right angles"$	$21. "Definition of right angles"$
$22. "Quad. " BCDF " is a rectangle"$	$22. "Quad. with 4 right angles is a rectangle"$

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

What is the missing statement in step 4?

$m ang AFB + m ang BFE = m ang AFE$
$90° + 90° = 180°$
$m ang AFB + 90° = 180°$
$90° + m ang BFE = 180°$

Question Info

Quadrilaterals Question

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