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Common Core Standard HSG-SRT.B.4 Questions

Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.

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

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What is the missing reason in step 9?
  1. Addition Property of Equality
  2. Transitive Property of Equality
  3. Subtraction Property of Equality
  4. Corresponding angles of congruent triangles are congruent
Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.4

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What is the missing statement in step 15?
  1. [math]Delta ABC \ ~ \ Delta ANM[/math]
  2. [math]Delta ABC \ ~ \ Delta AMN[/math]
  3. [math]Delta ABC \ ~ \ Delta MAN[/math]
  4. [math]Delta ABC \ ~ \ Delta MNA[/math]
Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.4

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What is the missing statement in step 14?
  1. [math]Delta ACD \ ~ \ Delta CAB[/math]
  2. [math]Delta ACD \ ~ \ Delta BCA[/math]
  3. [math]Delta ACD \ ~ \ Delta ABC[/math]
  4. [math]Delta ACD \ ~ \ Delta ACB[/math]
Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.4

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What is the missing reason in step 17?
  1. If two lines are cut by a transversal, and vertical angles are congruent, the two lines are parallel
  2. If two lines are cut by a transversal, and alternate exterior angles are congruent, the two lines are parallel
  3. If two lines are cut by a transversal, and corresponding angles are congruent, the two lines are parallel
  4. If two lines are cut by a transversal, and alternate interior angles are congruent, the two lines are parallel
Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.4

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What is the missing reason in step 18?
  1. Given
  2. Angle Addition Postulate
  3. Consecutive Interior Angles Postulate
  4. Sum of the acute angles in a right triangle is 90°
Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.4

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What is the missing statement in step 27?
  1. [math]Delta ABC \ ~ \ Delta CBD[/math]
  2. [math]Delta ABC \ ~ \ Delta CDB[/math]
  3. [math]Delta ABC \ ~ \ Delta DBC[/math]
  4. [math]Delta ABC \ ~ \ Delta DCB[/math]
Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.4

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What is the missing statement in step 28?
  1. [math](BC)/(BD) = (BC)/(AB)[/math]
  2. [math](BC)/(BD) = (AB)/(BC)[/math]
  3. [math](CD)/(AC) = (AB)/(BC)[/math]
  4. [math](AB)/(CD) = (AB)/(BC)[/math]
Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.4

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What is the missing statement in step 30?
  1. [math](CD)/(AB) = (AB)/(AC)[/math]
  2. [math](BC)/(AD) = (AB)/(AC)[/math]
  3. [math](AC)/(AD) = (AC)/(AB)[/math]
  4. [math](AC)/(AD) = (AB)/(AC)[/math]
Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.4

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What is the missing reason in step 32?
  1. Segment Addition Postulate
  2. Given
  3. Midpoint of a line segment
  4. Perpendicular Bisector Theorem
Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.4

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What is the missing reason in step 34?
  1. Binomial Expansion Theorem
  2. Addition Property of Equality
  3. Pythagorean Theorem
  4. Perimeter of a triangle
Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.4

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What is the missing reason in step 1?
  1. Parallel Postulate
  2. Given
  3. If two lines are cut by a transversal and alternate interior angles are supplementary, the lines are parallel
  4. If two lines are cut by a transversal and corresponding angles are congruent, the lines are parallel
Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.4

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What is the missing reason in step 3?
  1. Reflexive Property of Congruence
  2. Identity Property of Congruence
  3. Reflection Property of Congruence
  4. Given
Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.4

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What is the missing statement in step 4?
  1. [math]Delta BED \ ~ \ Delta ABC[/math]
  2. [math]Delta DEB \ ~ \ Delta ABC[/math]
  3. [math]Delta BDE \ ~ \ Delta ABC[/math]
  4. [math]Delta DBE \ ~ \ Delta ABC[/math]
Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.4

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What is the missing reason in step 8?
  1. Ratios of corresponding sides of similar triangles are equal
  2. Division Property of Equality
  3. Substitution Property of Equality
  4. Corresponding sides of congruent triangles are congruent
Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.4

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What is the missing statement in step 5?
  1. [math](AC)/(DE) = (AB)/(AD)[/math]
  2. [math](AB)/(AD) = (BC)/(BE)[/math]
  3. [math](BC)/(CE) = (AC)/(DE)[/math]
  4. [math](AB)/(BD) = (BC)/(BE)[/math]
Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.4

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What is the missing reason in step 3?
  1. Definition of a midpoint
  2. Given
  3. Segment Equality Postulate
  4. Substitution Property of Equality
Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.4

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What is the missing reason in step 6?
  1. Definition of a right triangle
  2. Pythagorean Identity
  3. Sum of angles in a triangle equals 180°
  4. Given
Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.4

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What is the missing reason in step 9?
  1. Definition of a midpoint
  2. Given
  3. Segment Addition Postulate
  4. Substitution Property of Equality
Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.4

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What is the missing reason in step 7?
  1. Given
  2. Angle Addition Postulate
  3. Consecutive Interior Angles Theorem
  4. Sum of the acute angles in a right triangle is 90°
Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.4

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What is the missing reason in step 14?
  1. Ratios of corresponding sides in similar triangles are equal
  2. Division Property of Equality
  3. Segment Division Postulate
  4. Transitive Property of Equality

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