Similar and Congruent Figures Question

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In the questions below, choose the correct missing statements and reasons from the following proof.

Let line

$l$ (not pictured) be parallel to side

$bar{AC}$ in

$Delta ABC$ . Line

$l$ intersects

$bar{AB}$ at point

$D$ (not pictured) and

$bar{BC}$ at point

$E$ (not pictured). Prove that

$(AD)/(BD) = (CE)/(BE)$ .

Equilateral Triangle ABC v1

$\ \ \ \ \ \ \ \ \ \ \ \ \mathbf{"Statement"} \ \ \ \ \ \ \ \ \ \ \ \$	$\mathbf{"Reason"}$
$1. l " \|\| " bar{AC}$	$1. ""$
$2. ang BDE ~= ang A$	$2. "If two \|\| lines cut by a transversal, corr. angles congruent"$
$3. ang B ~= ang B$	$3. ""$
$4.$	$4. "AA Similarity Theorem"$
$5.$	$5. "Ratios corr. sides of similar triangles are equal"$
$6. BD + AD = AB$	$6. "Segment Addition Postulate"$
$7. BE + CE = BC$	$7. "Segment Addition Postulate"$
$8. (BD + AD)/(BD) = (BE + CE)/(BE)$	$8. ""$
$9. (BD)/(BD) + (AD)/(BD) = (BE)/(BE) + (CE)/(BE)$	$9. "Algebra (addition of fractions)"$
$10. 1 + (AD)/(BD) = 1 + (CE)/(BE)$	$10. "Any non-zero quantity divided by itself equals 1"$
$11. (AD)/(BD) = (CE)/(BE)$	$11. "Subtraction Property of Equality"$

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

What is the missing statement in step 5?

$(AC)/(DE) = (AB)/(AD)$
$(AB)/(AD) = (BC)/(BE)$
$(BC)/(CE) = (AC)/(DE)$
$(AB)/(BD) = (BC)/(BE)$

Question Info

Similar and Congruent Figures Question

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