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Question Group Info

This question group is public and is used in 4 tests.

Author: nsharp1
No. Questions: 5
Created: Dec 27, 2020
Last Modified: 4 years ago

Proof: Midpoints form Seg || to 3rd side

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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

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

A.

What is the missing reason in step 3?

Definition of a midpoint
Given
Segment Equality Postulate
Substitution Property of Equality

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

B.

What is the missing reason in step 9?

Definition of a midpoint
Given
Segment Addition Postulate
Substitution Property of Equality

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

C.

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

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

D.

What is the missing statement in step 15?

$Delta ABC \ ~ \ Delta ANM$
$Delta ABC \ ~ \ Delta AMN$
$Delta ABC \ ~ \ Delta MAN$
$Delta ABC \ ~ \ Delta MNA$

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

E.

What is the missing reason in step 17?

If two lines are cut by a transversal, and vertical angles are congruent, the two lines are parallel
If two lines are cut by a transversal, and alternate exterior angles are congruent, the two lines are parallel
If two lines are cut by a transversal, and corresponding angles are congruent, the two lines are parallel
If two lines are cut by a transversal, and alternate interior angles are congruent, the two lines are parallel