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Common Core Standard HSG-CO.C.11 Questions

Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

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Grade 10 Quadrilaterals CCSS: HSG-CO.C.11

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What is the missing reason in step 10?
  1. Double Angle Identity
  2. Supplementary angles
  3. From the diagram
  4. Substitution Property of Equality
Grade 10 Quadrilaterals CCSS: HSG-CO.C.11

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What is the missing statement in step 14?
  1. BAD and CDA are right angles
  2. ¯BA¯AD
  3. ¯CD¯AD
  4. mBAD=mCDA
Grade 10 Quadrilaterals CCSS: HSG-CO.C.11

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What is the missing reason in step 15?
  1. Given
  2. Opposite sides of a parallelogram are parallel
  3. From the diagram
  4. Opposite sides of a rectangle are parallel
Grade 10 Quadrilaterals CCSS: HSG-CO.C.11

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What is the missing reason in step 20?
  1. Parallelogram with four right angles is a rectangle
  2. Image given is a rectangle
  3. Quadrilateral with opposite sides parallel and congruent is a rectangle
  4. QED
Grade 10 Quadrilaterals CCSS: HSG-CO.C.11
Rectangle ABCDFill in the reasons for the following proof.

Given that ABCD is a parallelogram and ¯BD¯AC (line segments not pictured) prove that ABCD is a rectangle.
             Statement             Reason
1.¯AC¯BD1.                                                                 
2.ABCD is a parallelogram2.
3.¯AB¯DC3.
4.¯AD¯AD4.
5.ΔABDΔDCA5.
6.BADCDA6.
7.¯AB || ¯CD7.
8.mBAD+mCDA=180°8.
9.mBAD=mCDA9.
10.mBAD+mBAD=180°10.
11.2mBAD=180°11.
12.mBAD=90°12.
13.mCDA=90°13.
14.BADandCDA are right angles14.
15.¯BC || ¯AD15.
16.mBAD+mABC=180°,      mADC+mDCB=180°16.
17.90°+mABC=180°,      90°+mDCB=180°17.
18.mABC=90°,      mDCB=90°18.
19.ABC,DCB are right angles19.
20.ABCD is a rectangle20.
Grade 10 Quadrilaterals CCSS: HSG-CO.C.11
What is the missing reason in step 8 of the following proof?

Given: Quadrilateral ABCD with diagonal ¯BD where ¯AB || ¯CD and ¯BC || ¯AD
Prove: BADDCB

Parallelogram ABCD v3

             Statement             Reason
1.¯AB || ¯CD1.Given
2.ABDCDB2.Alternate interior angles are congruent
3.¯BC || ¯AD3.Given
4.ADBCBD4.Alternate interior angles are congruent
5.mABD=mCDB,  mADB=mCBD5.Definition congruent angles
6.mABD+mADB+mBAD=180°,          mCDB+mDCB+mCBD=180°6.Sum of angles in a triangle is 180°
7.mCDB+mDCB+mCBD=           mABD+mADB+mBAD7.Substitution Property of Equality
8.mDCB=mBAD8.
9.BADDCB9.Definition of congruent angles
  1. Elimination Property of Equality
  2. Corresponding angles are congruent
  3. Definition of congruent terms
  4. Subtraction Property of Equality
Grade 10 Quadrilaterals CCSS: HSG-CO.C.11

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What is the missing statement in step 5?
  1. ΔABCΔDCB
  2. ΔABDΔDCA
  3. ΔADCΔACB
  4. ΔABDΔDCB
Grade 10 Quadrilaterals CCSS: HSG-CO.C.11

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What is the missing reason in step 8?
  1. Parallel Postulate
  2. Supplementary angles
  3. Same side interior angles are supplementary
  4. Linear Pairs are supplementary

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