Similar and Congruent Figures Question

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

In

$Delta ABC$ , let

$M$ (not pictured) be the midpoint of

$bar{AB}$ and

$N$ (not pictured) be the midpoint of

$bar{AC}$ . Prove that

$bar{MN} " || " bar{BC}$ .

Equilateral Triangle ABC v2

$\ \ \ \ \ \ \ \ \ \ \ \ \mathbf{"Statement"} \ \ \ \ \ \ \ \ \ \ \ \$	$\mathbf{"Reason"}$
$1. ang A ~= ang A$	$1. "Reflexive Property of Congruence"$
$2. M " is the midpoint of " bar{AB} \ \ \ \ \ \ \$	$2. "Given"$
$3. AM = BM$	$3. ""$
$4. AM + BM = AB$	$4. "Segment Addition Postulate"$
$5. AM + AM = AB$	$5. "Substitution Property of Equality"$
$6. 2 AM = AB$	$6. "Algebra (addition)"$
$7. (AM)/(AB) = 1/2$	$7. "Division Property of Equality"$
$8. N " is the midpoint of " bar{AC}$	$8. "Given"$
$9. AN = CN$	$9. ""$
$10.AN + CN = AC$	$10. "Segment Addition Postulate"$
$11. AN + AN = AC$	$11. "Substitution Property of Equality"$
$12. 2 AN = AC$	$12. "Algebra (addition)"$
$13. (AN)/(AC) = 1/2$	$13. "Division Property of Equality"$
$14. (AN)/(AC) = (AM)/(AB)$	$14. ""$
$15.$	$15. "SAS Similarity Theorem"$
$16. ang B ~= ang AMN$	$16. "Coor. angles in similar triangles congruent"$
$17. bar{BC} " \|\| " bar{MN}$	$17. ""$

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

What is the missing reason in step 14?

Ratios of corresponding sides in similar triangles are equal
Division Property of Equality
Segment Division Postulate
Transitive Property of Equality

Question Info

Similar and Congruent Figures Question

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